application in linear discriminant analysis.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"application in linear discriminant analysis.ipynb","provenance":[{"file_id":"1CnbOqwmJydQa8uCCpIR6HRVxw0YnveIP","timestamp":1591365193693}],"collapsed_sections":[],"toc_visible":true},"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.7.4"}},"cells":[{"cell_type":"markdown","metadata":{"id":"01Q1wGI3uIdg"},"source":["## libraries and function \n"]},{"cell_type":"code","metadata":{"id":"iEdO9dJPION8","executionInfo":{"status":"ok","timestamp":1604652402444,"user_tz":360,"elapsed":8009,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"8aab417a-ed78-450b-fda8-32817eccccb2","colab":{"base_uri":"https://localhost:8080/"}},"source":["!pip install impyute\n","from sklearn import datasets\n","from sklearn.preprocessing import LabelEncoder, StandardScaler, MinMaxScaler\n","from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as skLDA\n","from sklearn.experimental import enable_iterative_imputer\n","from sklearn.impute import IterativeImputer\n","from scipy import stats\n","import numpy as np\n","import impyute as impy\n","from fancyimpute import IterativeSVD, SoftImpute, NuclearNormMinimization\n","import pandas as pd\n","import time"],"execution_count":1,"outputs":[{"output_type":"stream","text":["Collecting impyute\n","  Downloading https://files.pythonhosted.org/packages/37/28/86829f67c9affb847facaab94687761d3555539ec675f7577778c5b2680a/impyute-0.0.8-py2.py3-none-any.whl\n","Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from impyute) (1.4.1)\n","Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from impyute) (1.18.5)\n","Requirement already satisfied: scikit-learn in /usr/local/lib/python3.6/dist-packages (from impyute) (0.22.2.post1)\n","Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.6/dist-packages (from scikit-learn->impyute) (0.17.0)\n","Installing collected packages: impyute\n","Successfully installed impyute-0.0.8\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/externals/six.py:31: FutureWarning: The module is deprecated in version 0.21 and will be removed in version 0.23 since we've dropped support for Python 2.7. Please rely on the official version of six (https://pypi.org/project/six/).\n","  \"(https://pypi.org/project/six/).\", FutureWarning)\n"],"name":"stderr"}]},{"cell_type":"markdown","metadata":{"id":"YxZbkGo8IOOS"},"source":["The function `mle` allows us to compute the MLEs from training data with monotone missing data.\n","\n","We denote\n","$$n = \\begin{pmatrix}\n","n_1^{(1)} & n_1^{(2)} &...&n_1^{(K)}\\\\\n","\\vdots & \\vdots &\\ddots&\\vdots\\\\\n","n_G^{(1)} & n_G^{(2)} &...&n_G^{(K)}\n","\\end{pmatrix}$$\n","$$p = (p_1,p_2,...,p_K)$$\n","G is the number of classes."]},{"cell_type":"markdown","metadata":{"id":"zJsxuiuVOWch"},"source":["### MLE function "]},{"cell_type":"code","metadata":{"id":"9iL76sKnIOOU","executionInfo":{"status":"ok","timestamp":1604652402448,"user_tz":360,"elapsed":6194,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}}},"source":["import numpy as np\n","def mle(Xtrain, n, p, G):\n","    '''\n","    Xtrain: list of input. The ith element of the list contains the sample from\n","    the ith class.\n","    '''\n","    if p[0]==1:\n","        # the array that contains the means of each block for the 1st block\n","        mus = [np.mean(Xtrain[g][:,0]) for g in np.arange(G)]\n","        S = [(n[g,0]-1)*np.var(Xtrain[g][:,0]) for g in np.arange(G)]\n","    else:\n","        mus = [np.mean(Xtrain[g][:,0:p[0]], axis = 0) for g  in np.arange(G)]\n","        S = [(n[g,0]-1)*np.cov(Xtrain[g][:,0:p[0]],rowvar =False) \n","             for g in np.arange(G)]\n","    \n","    mus = np.asarray(mus).T # so that each column is the mean of a class\n","    S = sum(S)/(sum(n[:,0])) \n","    S = S.reshape((p[0],-1))\n","    for i in np.arange(1,len(p)):\n","        W = [(n[g,i]-1)*np.cov(Xtrain[g][0:n[g,i],0:p[i]],\n","                              rowvar=False) for g in np.arange(G)]\n","        W = sum(W)\n","        \n","        P = np.matmul(W[(p[i-1]):p[i], 0:p[i-1]],\n","                      np.linalg.inv(W[0:p[i-1],0:p[i-1]]))\n","        Q = (W[p[i-1]:p[i],p[i-1]:p[i]]-\n","            np.matmul(P, W[0:p[i-1],p[i-1]:p[i]]))/sum(n[:,i])\n","        xmeans = [np.mean(Xtrain[g][0:n[g,i],0:p[i]], axis = 0) \n","                  for g in np.arange(G)]\n","        \n","        xmeans = np.asarray(xmeans)\n","        xmeans = xmeans.T\n","        mus = np.vstack((mus, xmeans[p[i-1]:p[i],:]\n","                       - np.matmul(P, xmeans[0:p[i-1]]-mus)))\n","        S21 = np.matmul(P, S)\n","        S = np.vstack((np.hstack((S, S21.T)),\n","                       np.hstack((S21, Q+np.matmul(P, S21.T)))))\n","    return [mus, S]"],"execution_count":2,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"5Kk3Z0jcObqQ"},"source":["### LDA and nan function \n"]},{"cell_type":"code","metadata":{"id":"V4-kNYKJIOOd","executionInfo":{"status":"ok","timestamp":1604652402450,"user_tz":360,"elapsed":2000,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}}},"source":["# function that return the misclassfication rate\n","# for LDA with missing data\n","def lda_miss(mus, S, Xtest, ytrain, ytest, G):\n","    f = lambda g: np.log(np.mean(ytrain==g)) - np.matmul(\n","                  np.matmul(mus[:,g].T, np.linalg.inv(S)), mus[:,g]/2)\n","    last2 = [f(g) for g in np.arange(G)]\n","    \n","    h = lambda g,i: last2[g] + np.matmul(mus[:,g].T, np.matmul(\n","                    np.linalg.inv(S), Xtest[i,:].T))\n","    pred_label = [np.argmax([h(g,i) for g in np.arange(G)]) \n","                  for i in np.arange(len(Xtest))]\n","    pred_label = np.asarray(pred_label)\n","    return np.mean(pred_label.flatten() != ytest)\n","\n","'''\n","function that create data list that contain missing values\n","The input X is a numpy array, y is the label\n","the function return a list where the ith element of \n","the list belongs to the ith class\n","'''\n","\n","def make_nan_list(X,y,G, n, p):\n","    # note that the label should go from 0 to G-1\n","    data = []\n","    for g in np.arange(G):\n","        data.append(X[y==g,:])\n","        for k in np.arange(len(p)-1):\n","            data[g][n[g,k+1]:n[g,k], p[k]:] = np.nan\n","    return data"],"execution_count":3,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"IwG2bsDOOxls"},"source":["### compute_err function "]},{"cell_type":"code","metadata":{"id":"8oXh1_ou0BPS","executionInfo":{"status":"ok","timestamp":1604652405051,"user_tz":360,"elapsed":815,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}}},"source":["def missing_rate(Xtrain, ytrain, Xtest, ytest, n, p, G):    \n","    Xtr_nan_list = make_nan_list(Xtrain,ytrain,G, n, p)\n","    # make NA data\n","    # since making function changes the order of observation\n","    # we need to generate new ytr from Xtr_nan    \n","    Xtr_nan, ytr = Xtr_nan_list[0], np.repeat(0, len(Xtr_nan_list[0]))\n","    for g in np.arange(1,G):\n","        Xtr_nan = np.vstack((Xtr_nan, Xtr_nan_list[g]))\n","        ytr = np.hstack((ytr, np.repeat(g, len(Xtr_nan_list[g]))))\n","\n","    # percentage of missing values\n","    per_missing = np.mean(np.isnan(Xtr_nan))\n","    return per_missing"],"execution_count":4,"outputs":[]},{"cell_type":"code","metadata":{"id":"ZEAkkeS5IOOo","executionInfo":{"status":"ok","timestamp":1604652406484,"user_tz":360,"elapsed":937,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}}},"source":["def compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G):    \n","    Xtr_nan_list = make_nan_list(Xtrain,ytrain,G, n, p)\n","    # make NA data\n","    # since making function changes the order of observation\n","    # we need to generate new ytr from Xtr_nan    \n","    Xtr_nan, ytr = Xtr_nan_list[0], np.repeat(0, len(Xtr_nan_list[0]))\n","    for g in np.arange(1,G):\n","        Xtr_nan = np.vstack((Xtr_nan, Xtr_nan_list[g]))\n","        ytr = np.hstack((ytr, np.repeat(g, len(Xtr_nan_list[g]))))\n","\n","    # percentage of missing values\n","    per_missing = np.mean(np.isnan(Xtr_nan))\n","\n","    scaler = MinMaxScaler()\n","    scaler.fit(Xtr_nan)\n","    Xtr_nan = scaler.transform(Xtr_nan)\n","    Xtest = scaler.transform(Xtest)\n","    Xtr_nan_list2 = []\n","    for g in range(G):\n","      Xtr_nan_list2.append(scaler.transform(Xtr_nan_list[g]))\n","\n","    # MLEs approach\n","    start = time.time()\n","    mus, S = mle(Xtr_nan_list2, n, p, G)\n","    mle_err = lda_miss(mus, S, Xtest, ytrain, ytest, G)\n","    mle_time = time.time()-start\n","    \n","    #impute,classify and get the error rates for imputation approaches    \n","    start = time.time()\n","    Xtr_em = impy.em(Xtr_nan)\n","    clf_em = skLDA().fit(Xtr_em, ytr)\n","    em_err = np.mean(clf_em.predict(Xtest).flatten() != ytest)\n","    em_time = time.time()-start \n","\n","    start = time.time()\n","    Xtr_knn = impy.fast_knn(Xtr_nan)\n","    clf_knn = skLDA().fit(Xtr_knn, ytr)\n","    knn_err = np.mean(clf_knn.predict(Xtest).flatten() != ytest)\n","    knn_time = time.time()-start \n","\n","    start = time.time()\n","    Xtr_softimpute = SoftImpute(max_iters = 100).fit_transform(Xtr_nan)\n","    clf_softimpute = skLDA().fit(Xtr_softimpute, ytr)\n","    softimpute_err = np.mean(clf_softimpute.predict(Xtest).flatten() != ytest)\n","    softimpute_time = time.time()-start\n","\n","    start = time.time()\n","    Xtr_mice = IterativeImputer(max_iter=100).fit(Xtr_nan).transform(Xtr_nan)\n","    clf_mice = skLDA().fit(Xtr_mice, ytr)\n","    mice_err = np.mean(clf_mice.predict(Xtest).flatten() != ytest)\n","    mice_time = time.time()-start\n","\n","    start = time.time()\n","    Xtr_nuclear = NuclearNormMinimization(max_iters=100).fit_transform(Xtr_nan)\n","    clf_nuclear = skLDA().fit(Xtr_nuclear, ytr)\n","    nuclear_err = np.mean(clf_nuclear.predict(Xtest).flatten() != ytest)\n","    nuclear_time = time.time()-start\n","    \n","    err_rate = np.array([mle_err, knn_err, mice_err, softimpute_err, em_err,\n","           nuclear_err, per_missing])\n","    return err_rate"],"execution_count":5,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"gzvE6YC4Iclj"},"source":["## Inosphere"]},{"cell_type":"code","metadata":{"id":"5Ile44T4IeyN","executionInfo":{"status":"ok","timestamp":1604652410827,"user_tz":360,"elapsed":928,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"c7c20125-24e2-436e-b2de-c80c67205ec6","colab":{"base_uri":"https://localhost:8080/"}},"source":["data = pd.read_csv('http://archive.ics.uci.edu/ml/machine-learning-databases/ionosphere/ionosphere.data',\n","                  sep = \",\", header = None)\n","print(data.head())\n","data = pd.DataFrame.to_numpy(data)\n","X, y = data[:,:34].astype(np.float64), data[:,34]\n","le2 = LabelEncoder()\n","y = le2.fit_transform(y)\n","print(len(y))\n","4/5*np.array([sum(y==0), sum(y==1)])"],"execution_count":6,"outputs":[{"output_type":"stream","text":["   0   1        2        3        4   ...       30       31       32       33  34\n","0   1   0  0.99539 -0.05889  0.85243  ...  0.42267 -0.54487  0.18641 -0.45300   g\n","1   1   0  1.00000 -0.18829  0.93035  ... -0.16626 -0.06288 -0.13738 -0.02447   b\n","2   1   0  1.00000 -0.03365  1.00000  ...  0.60436 -0.24180  0.56045 -0.38238   g\n","3   1   0  1.00000 -0.45161  1.00000  ...  0.25682  1.00000 -0.32382  1.00000   b\n","4   1   0  1.00000 -0.02401  0.94140  ... -0.05707 -0.59573 -0.04608 -0.65697   g\n","\n","[5 rows x 35 columns]\n","351\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([100.8, 180. ])"]},"metadata":{"tags":[]},"execution_count":6}]},{"cell_type":"code","metadata":{"id":"1ekhYbejIrEV","executionInfo":{"status":"ok","timestamp":1604652414305,"user_tz":360,"elapsed":1061,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"b88169d0-44ab-4df2-aa97-118bfd40c55b","colab":{"base_uri":"https://localhost:8080/"}},"source":["print(stats.describe(X[:,1]))\n","X = np.delete(X,[0,1], axis = 1)\n","X.shape"],"execution_count":7,"outputs":[{"output_type":"stream","text":["DescribeResult(nobs=351, minmax=(0.0, 0.0), mean=0.0, variance=0.0, skewness=0.0, kurtosis=-3.0)\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["(351, 32)"]},"metadata":{"tags":[]},"execution_count":7}]},{"cell_type":"markdown","metadata":{"id":"lytrJf32Isvw"},"source":["### 20%"]},{"cell_type":"code","metadata":{"id":"bLqVxbZ2I-_x","executionInfo":{"status":"ok","timestamp":1595214366127,"user_tz":300,"elapsed":96411,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"68696f89-48a1-4aac-ebe8-0cd279b61e48","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),100,90,76],\n","                  [sum(ytrain==1),180,150,90]])\n","    p = np.array([5,10,20,32])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,2) for k in np.arange(5)]\n","res20 = np.mean(np.asarray(res), axis=0)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 51.728363\n","[SoftImpute] Iter 1: observed MAE=0.048477 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.048656 rank=32\n","[SoftImpute] Iter 3: observed MAE=0.048757 rank=32\n","[SoftImpute] Iter 4: observed MAE=0.048820 rank=32\n","[SoftImpute] Iter 5: observed MAE=0.048858 rank=32\n","[SoftImpute] Iter 6: observed MAE=0.048883 rank=32\n","[SoftImpute] Iter 7: observed MAE=0.048900 rank=32\n","[SoftImpute] Iter 8: observed MAE=0.048913 rank=32\n","[SoftImpute] Iter 9: observed MAE=0.048922 rank=32\n","[SoftImpute] Iter 10: observed MAE=0.048931 rank=32\n","[SoftImpute] Iter 11: observed MAE=0.048938 rank=32\n","[SoftImpute] Iter 12: observed MAE=0.048943 rank=32\n","[SoftImpute] Iter 13: observed MAE=0.048948 rank=32\n","[SoftImpute] Iter 14: observed MAE=0.048954 rank=32\n","[SoftImpute] Iter 15: observed MAE=0.048958 rank=32\n","[SoftImpute] Iter 16: observed MAE=0.048962 rank=32\n","[SoftImpute] Iter 17: observed MAE=0.048966 rank=32\n","[SoftImpute] Iter 18: observed MAE=0.048968 rank=31\n","[SoftImpute] Iter 19: observed MAE=0.048969 rank=31\n","[SoftImpute] Iter 20: observed MAE=0.048971 rank=31\n","[SoftImpute] Iter 21: observed MAE=0.048972 rank=31\n","[SoftImpute] Iter 22: observed MAE=0.048973 rank=31\n","[SoftImpute] Iter 23: observed MAE=0.048974 rank=31\n","[SoftImpute] Iter 24: observed MAE=0.048974 rank=31\n","[SoftImpute] Iter 25: observed MAE=0.048974 rank=31\n","[SoftImpute] Iter 26: observed MAE=0.048974 rank=31\n","[SoftImpute] Iter 27: observed MAE=0.048974 rank=31\n","[SoftImpute] Iter 28: observed MAE=0.048974 rank=31\n","[SoftImpute] Iter 29: observed MAE=0.048974 rank=31\n","[SoftImpute] Iter 30: observed MAE=0.048975 rank=31\n","[SoftImpute] Iter 31: observed MAE=0.048976 rank=31\n","[SoftImpute] Iter 32: observed 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observed MAE=0.048987 rank=31\n","[SoftImpute] Iter 51: observed MAE=0.048988 rank=31\n","[SoftImpute] Iter 52: observed MAE=0.048988 rank=31\n","[SoftImpute] Iter 53: observed MAE=0.048989 rank=31\n","[SoftImpute] Iter 54: observed MAE=0.048989 rank=31\n","[SoftImpute] Iter 55: observed MAE=0.048989 rank=31\n","[SoftImpute] Iter 56: observed MAE=0.048990 rank=31\n","[SoftImpute] Iter 57: observed MAE=0.048990 rank=31\n","[SoftImpute] Iter 58: observed MAE=0.048990 rank=31\n","[SoftImpute] Iter 59: observed MAE=0.048991 rank=31\n","[SoftImpute] Iter 60: observed MAE=0.048991 rank=31\n","[SoftImpute] Iter 61: observed MAE=0.048991 rank=31\n","[SoftImpute] Iter 62: observed MAE=0.048991 rank=31\n","[SoftImpute] Iter 63: observed MAE=0.048992 rank=31\n","[SoftImpute] Iter 64: observed MAE=0.048992 rank=31\n","[SoftImpute] Iter 65: observed MAE=0.048992 rank=31\n","[SoftImpute] Iter 66: observed MAE=0.048992 rank=31\n","[SoftImpute] Iter 67: observed MAE=0.048993 rank=31\n","[SoftImpute] Iter 68: observed MAE=0.048993 rank=31\n","[SoftImpute] Iter 69: observed MAE=0.048993 rank=31\n","[SoftImpute] Iter 70: observed MAE=0.048993 rank=31\n","[SoftImpute] Iter 71: observed MAE=0.048994 rank=31\n","[SoftImpute] Iter 72: observed MAE=0.048994 rank=31\n","[SoftImpute] Iter 73: observed MAE=0.048994 rank=31\n","[SoftImpute] Iter 74: observed MAE=0.048994 rank=31\n","[SoftImpute] Iter 75: observed MAE=0.048994 rank=31\n","[SoftImpute] Iter 76: observed MAE=0.048995 rank=31\n","[SoftImpute] Iter 77: observed MAE=0.048995 rank=31\n","[SoftImpute] Iter 78: observed MAE=0.048995 rank=31\n","[SoftImpute] Iter 79: observed MAE=0.048995 rank=31\n","[SoftImpute] Stopped after iteration 79 for lambda=1.034567\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 106040\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 65250, constraints m = 82914\n","Cones:\tprimal zero / dual free vars: 8832\n","\tlinear vars: 26496\n","\tsd vars: 47586, sd blks: 1\n","Setup time: 9.02e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.16e+21  3.05e+21  1.00e+00 -1.65e+24  3.44e+23  5.67e+23  6.22e-02 \n","   100| 1.94e-03  3.00e-03  1.93e-04  1.59e+02  1.59e+02  2.29e-14  8.25e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.25e+00s\n","\tLin-sys: nnz in L factor: 261351, avg solve time: 1.75e-03s\n","\tCones: avg projection time: 5.43e-02s\n","\tAcceleration: avg step time: 2.18e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.5849e-09, dist(y, K*) = 2.6393e-09, s'y/|s||y| = -7.9587e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.9550e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.7478e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 8.6573e-05\n","----------------------------------------------------------------------------\n","c'x = 159.0520, -b'y = 159.0244\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 52.200649\n","[SoftImpute] Iter 1: observed MAE=0.048274 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.048481 rank=32\n","[SoftImpute] Iter 3: observed MAE=0.048598 rank=32\n","[SoftImpute] Iter 4: observed MAE=0.048673 rank=32\n","[SoftImpute] Iter 5: observed MAE=0.048722 rank=32\n","[SoftImpute] Iter 6: observed MAE=0.048754 rank=32\n","[SoftImpute] Iter 7: observed MAE=0.048774 rank=32\n","[SoftImpute] Iter 8: observed MAE=0.048789 rank=32\n","[SoftImpute] Iter 9: observed MAE=0.048799 rank=32\n","[SoftImpute] Iter 10: observed MAE=0.048808 rank=32\n","[SoftImpute] Iter 11: observed MAE=0.048815 rank=32\n","[SoftImpute] Iter 12: observed MAE=0.048823 rank=32\n","[SoftImpute] Iter 13: observed MAE=0.048830 rank=32\n","[SoftImpute] Iter 14: observed MAE=0.048837 rank=32\n","[SoftImpute] Iter 15: observed MAE=0.048843 rank=32\n","[SoftImpute] Iter 16: observed MAE=0.048849 rank=32\n","[SoftImpute] Iter 17: observed MAE=0.048855 rank=32\n","[SoftImpute] Iter 18: observed MAE=0.048860 rank=32\n","[SoftImpute] Iter 19: observed MAE=0.048866 rank=32\n","[SoftImpute] Iter 20: observed MAE=0.048871 rank=32\n","[SoftImpute] Iter 21: observed MAE=0.048876 rank=32\n","[SoftImpute] Iter 22: observed MAE=0.048880 rank=32\n","[SoftImpute] Iter 23: observed MAE=0.048884 rank=32\n","[SoftImpute] Iter 24: observed MAE=0.048887 rank=32\n","[SoftImpute] Iter 25: observed MAE=0.048891 rank=32\n","[SoftImpute] Iter 26: observed MAE=0.048895 rank=32\n","[SoftImpute] Iter 27: observed MAE=0.048899 rank=32\n","[SoftImpute] Iter 28: observed MAE=0.048903 rank=32\n","[SoftImpute] Iter 29: observed MAE=0.048907 rank=32\n","[SoftImpute] Iter 30: observed MAE=0.048911 rank=32\n","[SoftImpute] Iter 31: observed MAE=0.048914 rank=32\n","[SoftImpute] Iter 32: observed MAE=0.048918 rank=32\n","[SoftImpute] Iter 33: observed MAE=0.048921 rank=32\n","[SoftImpute] Iter 34: observed MAE=0.048925 rank=32\n","[SoftImpute] Iter 35: observed MAE=0.048928 rank=32\n","[SoftImpute] Iter 36: observed MAE=0.048931 rank=32\n","[SoftImpute] Iter 37: observed MAE=0.048933 rank=32\n","[SoftImpute] Iter 38: observed MAE=0.048935 rank=32\n","[SoftImpute] Iter 39: observed MAE=0.048937 rank=32\n","[SoftImpute] Iter 40: observed MAE=0.048939 rank=32\n","[SoftImpute] Iter 41: observed MAE=0.048942 rank=32\n","[SoftImpute] Iter 42: observed MAE=0.048943 rank=32\n","[SoftImpute] Iter 43: observed MAE=0.048945 rank=32\n","[SoftImpute] Iter 44: observed MAE=0.048947 rank=32\n","[SoftImpute] Iter 45: observed MAE=0.048948 rank=32\n","[SoftImpute] Iter 46: observed MAE=0.048950 rank=32\n","[SoftImpute] Iter 47: observed MAE=0.048951 rank=32\n","[SoftImpute] Iter 48: observed MAE=0.048953 rank=32\n","[SoftImpute] Iter 49: observed MAE=0.048954 rank=32\n","[SoftImpute] Iter 50: observed MAE=0.048955 rank=32\n","[SoftImpute] Iter 51: observed MAE=0.048956 rank=32\n","[SoftImpute] Iter 52: observed MAE=0.048957 rank=32\n","[SoftImpute] Iter 53: observed MAE=0.048958 rank=32\n","[SoftImpute] Iter 54: observed MAE=0.048958 rank=32\n","[SoftImpute] Iter 55: observed MAE=0.048959 rank=32\n","[SoftImpute] Iter 56: observed MAE=0.048960 rank=32\n","[SoftImpute] Iter 57: observed MAE=0.048960 rank=32\n","[SoftImpute] Iter 58: observed MAE=0.048961 rank=32\n","[SoftImpute] Iter 59: observed MAE=0.048961 rank=32\n","[SoftImpute] Iter 60: observed MAE=0.048961 rank=32\n","[SoftImpute] Iter 61: observed MAE=0.048961 rank=32\n","[SoftImpute] Iter 62: observed MAE=0.048962 rank=32\n","[SoftImpute] Iter 63: observed MAE=0.048962 rank=32\n","[SoftImpute] Iter 64: observed MAE=0.048962 rank=32\n","[SoftImpute] Iter 65: observed MAE=0.048963 rank=32\n","[SoftImpute] Iter 66: observed MAE=0.048963 rank=32\n","[SoftImpute] Iter 67: observed MAE=0.048963 rank=32\n","[SoftImpute] Iter 68: observed MAE=0.048963 rank=32\n","[SoftImpute] Iter 69: observed MAE=0.048963 rank=32\n","[SoftImpute] Iter 70: observed MAE=0.048964 rank=32\n","[SoftImpute] Iter 71: observed MAE=0.048964 rank=32\n","[SoftImpute] Iter 72: observed MAE=0.048964 rank=32\n","[SoftImpute] Iter 73: observed MAE=0.048964 rank=32\n","[SoftImpute] Iter 74: observed MAE=0.048964 rank=32\n","[SoftImpute] Iter 75: observed MAE=0.048964 rank=32\n","[SoftImpute] Iter 76: observed MAE=0.048964 rank=32\n","[SoftImpute] Iter 77: observed MAE=0.048965 rank=32\n","[SoftImpute] Iter 78: observed MAE=0.048965 rank=32\n","[SoftImpute] Iter 79: observed MAE=0.048965 rank=32\n","[SoftImpute] Iter 80: observed MAE=0.048965 rank=32\n","[SoftImpute] Iter 81: observed MAE=0.048965 rank=32\n","[SoftImpute] Iter 82: observed MAE=0.048965 rank=32\n","[SoftImpute] Iter 83: observed MAE=0.048965 rank=32\n","[SoftImpute] Stopped after iteration 83 for lambda=1.044013\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 108939\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 67503, constraints m = 85551\n","Cones:\tprimal zero / dual free vars: 9024\n","\tlinear vars: 27072\n","\tsd vars: 49455, sd blks: 1\n","Setup time: 8.94e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.23e+21  3.12e+21  1.00e+00 -1.71e+24  3.56e+23  5.82e+23  5.66e-02 \n","   100| 3.82e-03  7.19e-03  1.18e-03  1.56e+02  1.56e+02  3.82e-14  9.13e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 9.13e+00s\n","\tLin-sys: nnz in L factor: 269175, avg solve time: 1.83e-03s\n","\tCones: avg projection time: 6.19e-02s\n","\tAcceleration: avg step time: 2.27e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7222e-09, dist(y, K*) = 6.2906e-08, s'y/|s||y| = -2.1021e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.3995e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.2127e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.8160e-04\n","----------------------------------------------------------------------------\n","c'x = 155.8451, -b'y = 155.7883\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 51.934672\n","[SoftImpute] Iter 1: observed MAE=0.047902 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.048188 rank=32\n","[SoftImpute] Iter 3: observed MAE=0.048342 rank=32\n","[SoftImpute] Iter 4: observed MAE=0.048424 rank=32\n","[SoftImpute] Iter 5: observed MAE=0.048469 rank=32\n","[SoftImpute] Iter 6: observed MAE=0.048495 rank=32\n","[SoftImpute] Iter 7: observed MAE=0.048512 rank=32\n","[SoftImpute] Iter 8: observed MAE=0.048524 rank=32\n","[SoftImpute] Iter 9: observed MAE=0.048536 rank=32\n","[SoftImpute] Iter 10: observed MAE=0.048546 rank=32\n","[SoftImpute] Iter 11: observed MAE=0.048555 rank=32\n","[SoftImpute] Iter 12: observed MAE=0.048563 rank=32\n","[SoftImpute] Iter 13: observed MAE=0.048570 rank=32\n","[SoftImpute] Iter 14: observed MAE=0.048577 rank=32\n","[SoftImpute] Iter 15: observed MAE=0.048582 rank=32\n","[SoftImpute] Iter 16: observed MAE=0.048587 rank=32\n","[SoftImpute] Iter 17: observed MAE=0.048591 rank=32\n","[SoftImpute] Iter 18: observed MAE=0.048595 rank=32\n","[SoftImpute] Iter 19: observed MAE=0.048598 rank=32\n","[SoftImpute] Iter 20: observed MAE=0.048601 rank=32\n","[SoftImpute] Iter 21: observed MAE=0.048603 rank=32\n","[SoftImpute] Iter 22: observed MAE=0.048605 rank=32\n","[SoftImpute] Iter 23: observed MAE=0.048606 rank=32\n","[SoftImpute] Iter 24: observed MAE=0.048607 rank=32\n","[SoftImpute] Iter 25: observed MAE=0.048608 rank=32\n","[SoftImpute] Iter 26: observed MAE=0.048609 rank=32\n","[SoftImpute] Iter 27: observed MAE=0.048610 rank=32\n","[SoftImpute] Iter 28: observed MAE=0.048610 rank=32\n","[SoftImpute] Iter 29: observed MAE=0.048610 rank=32\n","[SoftImpute] Iter 30: observed MAE=0.048610 rank=32\n","[SoftImpute] Iter 31: observed MAE=0.048610 rank=32\n","[SoftImpute] Iter 32: observed MAE=0.048609 rank=32\n","[SoftImpute] Iter 33: observed MAE=0.048609 rank=32\n","[SoftImpute] Iter 34: observed MAE=0.048608 rank=32\n","[SoftImpute] Iter 35: observed MAE=0.048607 rank=32\n","[SoftImpute] Iter 36: observed MAE=0.048606 rank=32\n","[SoftImpute] Iter 37: observed MAE=0.048605 rank=32\n","[SoftImpute] Iter 38: observed MAE=0.048604 rank=32\n","[SoftImpute] Iter 39: observed MAE=0.048603 rank=32\n","[SoftImpute] Iter 40: observed MAE=0.048602 rank=32\n","[SoftImpute] Iter 41: observed MAE=0.048601 rank=32\n","[SoftImpute] Iter 42: observed MAE=0.048600 rank=32\n","[SoftImpute] Iter 43: observed MAE=0.048600 rank=32\n","[SoftImpute] Iter 44: observed MAE=0.048599 rank=32\n","[SoftImpute] Iter 45: observed MAE=0.048597 rank=32\n","[SoftImpute] Iter 46: observed MAE=0.048596 rank=32\n","[SoftImpute] Iter 47: observed MAE=0.048595 rank=32\n","[SoftImpute] Iter 48: observed MAE=0.048595 rank=32\n","[SoftImpute] Iter 49: observed MAE=0.048594 rank=32\n","[SoftImpute] Iter 50: observed MAE=0.048593 rank=32\n","[SoftImpute] Iter 51: observed MAE=0.048592 rank=32\n","[SoftImpute] Iter 52: observed MAE=0.048592 rank=32\n","[SoftImpute] Iter 53: observed MAE=0.048591 rank=32\n","[SoftImpute] Iter 54: observed MAE=0.048590 rank=32\n","[SoftImpute] Iter 55: observed MAE=0.048590 rank=32\n","[SoftImpute] Iter 56: observed MAE=0.048589 rank=32\n","[SoftImpute] Iter 57: observed MAE=0.048589 rank=32\n","[SoftImpute] Iter 58: observed MAE=0.048588 rank=32\n","[SoftImpute] Iter 59: observed MAE=0.048587 rank=32\n","[SoftImpute] Iter 60: observed MAE=0.048587 rank=32\n","[SoftImpute] Iter 61: observed MAE=0.048586 rank=32\n","[SoftImpute] Iter 62: observed MAE=0.048585 rank=32\n","[SoftImpute] Iter 63: observed MAE=0.048585 rank=32\n","[SoftImpute] Iter 64: observed MAE=0.048584 rank=32\n","[SoftImpute] Iter 65: observed MAE=0.048583 rank=32\n","[SoftImpute] Iter 66: observed MAE=0.048583 rank=32\n","[SoftImpute] Iter 67: observed MAE=0.048582 rank=32\n","[SoftImpute] Iter 68: observed MAE=0.048581 rank=32\n","[SoftImpute] Iter 69: observed MAE=0.048581 rank=32\n","[SoftImpute] Iter 70: observed MAE=0.048580 rank=32\n","[SoftImpute] Iter 71: observed MAE=0.048580 rank=32\n","[SoftImpute] Iter 72: observed MAE=0.048579 rank=32\n","[SoftImpute] Iter 73: observed MAE=0.048579 rank=32\n","[SoftImpute] Iter 74: observed MAE=0.048579 rank=32\n","[SoftImpute] Iter 75: observed MAE=0.048578 rank=32\n","[SoftImpute] Iter 76: observed MAE=0.048578 rank=32\n","[SoftImpute] Iter 77: observed MAE=0.048577 rank=32\n","[SoftImpute] Iter 78: observed MAE=0.048577 rank=32\n","[SoftImpute] Iter 79: observed MAE=0.048577 rank=32\n","[SoftImpute] Iter 80: observed MAE=0.048576 rank=32\n","[SoftImpute] Iter 81: observed MAE=0.048576 rank=32\n","[SoftImpute] Iter 82: observed MAE=0.048576 rank=32\n","[SoftImpute] Stopped after iteration 82 for lambda=1.038693\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 109940\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 68262, constraints m = 86438\n","Cones:\tprimal zero / dual free vars: 9088\n","\tlinear vars: 27264\n","\tsd vars: 50086, sd blks: 1\n","Setup time: 9.21e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.25e+21  3.14e+21  1.00e+00 -1.72e+24  3.57e+23  5.83e+23  5.29e-02 \n","   100| 1.56e-03  1.70e-03  3.51e-04  1.55e+02  1.55e+02  3.33e-14  8.96e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.97e+00s\n","\tLin-sys: nnz in L factor: 271847, avg solve time: 1.86e-03s\n","\tCones: avg projection time: 6.01e-02s\n","\tAcceleration: avg step time: 2.29e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7783e-09, dist(y, K*) = 7.7408e-09, s'y/|s||y| = 5.2914e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.4232e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.1998e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.0105e-04\n","----------------------------------------------------------------------------\n","c'x = 155.0266, -b'y = 154.9952\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 52.056740\n","[SoftImpute] Iter 1: observed MAE=0.048190 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.048450 rank=32\n","[SoftImpute] Iter 3: observed MAE=0.048592 rank=32\n","[SoftImpute] Iter 4: observed MAE=0.048671 rank=32\n","[SoftImpute] Iter 5: observed MAE=0.048719 rank=32\n","[SoftImpute] Iter 6: observed MAE=0.048750 rank=32\n","[SoftImpute] Iter 7: observed MAE=0.048772 rank=32\n","[SoftImpute] Iter 8: observed MAE=0.048789 rank=32\n","[SoftImpute] Iter 9: observed MAE=0.048802 rank=32\n","[SoftImpute] Iter 10: observed MAE=0.048815 rank=32\n","[SoftImpute] Iter 11: observed MAE=0.048825 rank=32\n","[SoftImpute] Iter 12: observed MAE=0.048835 rank=32\n","[SoftImpute] Iter 13: observed MAE=0.048844 rank=32\n","[SoftImpute] Iter 14: observed MAE=0.048851 rank=32\n","[SoftImpute] Iter 15: observed MAE=0.048858 rank=32\n","[SoftImpute] Iter 16: observed MAE=0.048864 rank=32\n","[SoftImpute] Iter 17: observed MAE=0.048869 rank=32\n","[SoftImpute] Iter 18: observed MAE=0.048874 rank=32\n","[SoftImpute] Iter 19: observed MAE=0.048878 rank=32\n","[SoftImpute] Iter 20: observed MAE=0.048882 rank=32\n","[SoftImpute] Iter 21: observed MAE=0.048886 rank=32\n","[SoftImpute] Iter 22: observed MAE=0.048890 rank=32\n","[SoftImpute] Iter 23: observed MAE=0.048894 rank=32\n","[SoftImpute] Iter 24: observed MAE=0.048897 rank=32\n","[SoftImpute] Iter 25: observed MAE=0.048901 rank=32\n","[SoftImpute] Iter 26: observed MAE=0.048905 rank=32\n","[SoftImpute] Iter 27: observed MAE=0.048909 rank=32\n","[SoftImpute] Iter 28: observed MAE=0.048912 rank=32\n","[SoftImpute] Iter 29: observed MAE=0.048917 rank=32\n","[SoftImpute] Iter 30: observed MAE=0.048921 rank=32\n","[SoftImpute] Iter 31: observed 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observed MAE=0.048985 rank=32\n","[SoftImpute] Iter 50: observed MAE=0.048987 rank=32\n","[SoftImpute] Iter 51: observed MAE=0.048990 rank=32\n","[SoftImpute] Iter 52: observed MAE=0.048992 rank=32\n","[SoftImpute] Iter 53: observed MAE=0.048994 rank=32\n","[SoftImpute] Iter 54: observed MAE=0.048997 rank=32\n","[SoftImpute] Iter 55: observed MAE=0.048998 rank=32\n","[SoftImpute] Iter 56: observed MAE=0.049000 rank=32\n","[SoftImpute] Iter 57: observed MAE=0.049002 rank=32\n","[SoftImpute] Iter 58: observed MAE=0.049004 rank=32\n","[SoftImpute] Iter 59: observed MAE=0.049005 rank=32\n","[SoftImpute] Iter 60: observed MAE=0.049006 rank=32\n","[SoftImpute] Iter 61: observed MAE=0.049008 rank=32\n","[SoftImpute] Iter 62: observed MAE=0.049009 rank=32\n","[SoftImpute] Iter 63: observed MAE=0.049010 rank=32\n","[SoftImpute] Iter 64: observed MAE=0.049011 rank=32\n","[SoftImpute] Iter 65: observed MAE=0.049012 rank=32\n","[SoftImpute] Iter 66: observed MAE=0.049013 rank=32\n","[SoftImpute] Iter 67: observed MAE=0.049014 rank=32\n","[SoftImpute] Iter 68: observed MAE=0.049015 rank=32\n","[SoftImpute] Iter 69: observed MAE=0.049016 rank=32\n","[SoftImpute] Iter 70: observed MAE=0.049017 rank=32\n","[SoftImpute] Iter 71: observed MAE=0.049017 rank=32\n","[SoftImpute] Iter 72: observed MAE=0.049018 rank=32\n","[SoftImpute] Iter 73: observed MAE=0.049019 rank=32\n","[SoftImpute] Iter 74: observed MAE=0.049019 rank=32\n","[SoftImpute] Iter 75: observed MAE=0.049020 rank=32\n","[SoftImpute] Iter 76: observed MAE=0.049020 rank=32\n","[SoftImpute] Iter 77: observed MAE=0.049021 rank=32\n","[SoftImpute] Iter 78: observed MAE=0.049021 rank=32\n","[SoftImpute] Iter 79: observed MAE=0.049022 rank=32\n","[SoftImpute] Iter 80: observed MAE=0.049022 rank=32\n","[SoftImpute] Iter 81: observed MAE=0.049023 rank=32\n","[SoftImpute] Iter 82: observed MAE=0.049023 rank=32\n","[SoftImpute] Iter 83: observed MAE=0.049023 rank=32\n","[SoftImpute] Stopped after iteration 83 for lambda=1.041135\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 112395\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 70177, constraints m = 88673\n","Cones:\tprimal zero / dual free vars: 9248\n","\tlinear vars: 27744\n","\tsd vars: 51681, sd blks: 1\n","Setup time: 8.74e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.30e+21  3.19e+21  1.00e+00 -1.78e+24  3.68e+23  5.99e+23  5.55e-02 \n","   100| 5.24e-04  7.88e-04  2.03e-04  1.60e+02  1.60e+02  2.13e-14  9.48e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 9.48e+00s\n","\tLin-sys: nnz in L factor: 278482, avg solve time: 1.82e-03s\n","\tCones: avg projection time: 6.43e-02s\n","\tAcceleration: avg step time: 2.36e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6684e-09, dist(y, K*) = 9.2031e-09, s'y/|s||y| = 4.0323e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.7371e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.4405e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.5973e-04\n","----------------------------------------------------------------------------\n","c'x = 159.5057, -b'y = 159.4226\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 52.203095\n","[SoftImpute] Iter 1: observed MAE=0.048947 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.049084 rank=32\n","[SoftImpute] Iter 3: observed MAE=0.049157 rank=32\n","[SoftImpute] Iter 4: observed MAE=0.049199 rank=32\n","[SoftImpute] Iter 5: observed MAE=0.049225 rank=32\n","[SoftImpute] Iter 6: observed MAE=0.049246 rank=32\n","[SoftImpute] Iter 7: observed MAE=0.049265 rank=32\n","[SoftImpute] Iter 8: observed MAE=0.049281 rank=32\n","[SoftImpute] Iter 9: observed MAE=0.049296 rank=32\n","[SoftImpute] Iter 10: observed MAE=0.049309 rank=32\n","[SoftImpute] Iter 11: observed MAE=0.049322 rank=32\n","[SoftImpute] Iter 12: observed MAE=0.049334 rank=32\n","[SoftImpute] Iter 13: observed MAE=0.049344 rank=32\n","[SoftImpute] Iter 14: observed MAE=0.049353 rank=32\n","[SoftImpute] Iter 15: observed MAE=0.049361 rank=32\n","[SoftImpute] Iter 16: observed MAE=0.049367 rank=32\n","[SoftImpute] Iter 17: observed MAE=0.049374 rank=32\n","[SoftImpute] Iter 18: observed MAE=0.049380 rank=32\n","[SoftImpute] Iter 19: observed MAE=0.049386 rank=32\n","[SoftImpute] Iter 20: observed MAE=0.049391 rank=32\n","[SoftImpute] Iter 21: observed MAE=0.049395 rank=32\n","[SoftImpute] Iter 22: observed MAE=0.049399 rank=32\n","[SoftImpute] Iter 23: observed MAE=0.049402 rank=32\n","[SoftImpute] Iter 24: observed MAE=0.049405 rank=32\n","[SoftImpute] Iter 25: observed MAE=0.049409 rank=32\n","[SoftImpute] Iter 26: observed MAE=0.049412 rank=32\n","[SoftImpute] Iter 27: observed MAE=0.049415 rank=32\n","[SoftImpute] Iter 28: observed MAE=0.049417 rank=32\n","[SoftImpute] Iter 29: observed MAE=0.049419 rank=32\n","[SoftImpute] Iter 30: observed MAE=0.049420 rank=32\n","[SoftImpute] Iter 31: observed MAE=0.049422 rank=32\n","[SoftImpute] Iter 32: observed MAE=0.049423 rank=32\n","[SoftImpute] Iter 33: observed MAE=0.049424 rank=32\n","[SoftImpute] Iter 34: observed MAE=0.049424 rank=32\n","[SoftImpute] Iter 35: observed MAE=0.049424 rank=32\n","[SoftImpute] 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rank=32\n","[SoftImpute] Iter 54: observed MAE=0.049403 rank=32\n","[SoftImpute] Iter 55: observed MAE=0.049401 rank=32\n","[SoftImpute] Iter 56: observed MAE=0.049400 rank=32\n","[SoftImpute] Iter 57: observed MAE=0.049399 rank=32\n","[SoftImpute] Iter 58: observed MAE=0.049397 rank=32\n","[SoftImpute] Iter 59: observed MAE=0.049396 rank=32\n","[SoftImpute] Iter 60: observed MAE=0.049394 rank=32\n","[SoftImpute] Iter 61: observed MAE=0.049393 rank=32\n","[SoftImpute] Iter 62: observed MAE=0.049392 rank=32\n","[SoftImpute] Iter 63: observed MAE=0.049390 rank=32\n","[SoftImpute] Iter 64: observed MAE=0.049389 rank=32\n","[SoftImpute] Iter 65: observed MAE=0.049388 rank=32\n","[SoftImpute] Iter 66: observed MAE=0.049387 rank=32\n","[SoftImpute] Iter 67: observed MAE=0.049386 rank=32\n","[SoftImpute] Iter 68: observed MAE=0.049385 rank=32\n","[SoftImpute] Iter 69: observed MAE=0.049384 rank=32\n","[SoftImpute] Iter 70: observed MAE=0.049383 rank=32\n","[SoftImpute] Iter 71: observed MAE=0.049382 rank=32\n","[SoftImpute] Iter 72: observed MAE=0.049382 rank=32\n","[SoftImpute] Iter 73: observed MAE=0.049381 rank=32\n","[SoftImpute] Iter 74: observed MAE=0.049381 rank=32\n","[SoftImpute] Iter 75: observed MAE=0.049380 rank=32\n","[SoftImpute] Iter 76: observed MAE=0.049380 rank=32\n","[SoftImpute] Iter 77: observed MAE=0.049379 rank=32\n","[SoftImpute] Iter 78: observed MAE=0.049379 rank=32\n","[SoftImpute] Stopped after iteration 78 for lambda=1.044062\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 104589\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 64137, constraints m = 81609\n","Cones:\tprimal zero / dual free vars: 8736\n","\tlinear vars: 26208\n","\tsd vars: 46665, sd blks: 1\n","Setup time: 8.52e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.13e+21  3.02e+21  1.00e+00 -1.64e+24  3.42e+23  5.65e+23  5.25e-02 \n","   100| 2.71e-03  4.26e-03  4.35e-05  1.59e+02  1.59e+02  9.85e-14  8.71e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.71e+00s\n","\tLin-sys: nnz in L factor: 257457, avg solve time: 1.67e-03s\n","\tCones: avg projection time: 5.94e-02s\n","\tAcceleration: avg step time: 2.15e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.3816e-09, dist(y, K*) = 1.3051e-08, s'y/|s||y| = -1.3510e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.9770e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.6711e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.4561e-05\n","----------------------------------------------------------------------------\n","c'x = 159.1898, -b'y = 159.1944\n","============================================================================\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"7PwB9Q0lJBpI"},"source":["### 30%"]},{"cell_type":"code","metadata":{"id":"RyM_4JVLJDbL","executionInfo":{"status":"ok","timestamp":1595215903092,"user_tz":300,"elapsed":103733,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"437a4a33-fa26-467a-c254-9185cb3e73a9","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(0)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),100,75,67],\n","                  [sum(ytrain==1),150,120,90]])\n","    p = np.array([5,10,15,32])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,2) for k in np.arange(5)]\n","res30 = np.mean(np.asarray(res), axis=0)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 48.418082\n","[SoftImpute] Iter 1: observed MAE=0.048273 rank=31\n","[SoftImpute] Iter 2: observed MAE=0.048462 rank=31\n","[SoftImpute] Iter 3: observed MAE=0.048600 rank=31\n","[SoftImpute] Iter 4: observed MAE=0.048695 rank=31\n","[SoftImpute] Iter 5: observed MAE=0.048759 rank=31\n","[SoftImpute] Iter 6: observed MAE=0.048806 rank=31\n","[SoftImpute] Iter 7: observed 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rank=30\n","[SoftImpute] Iter 61: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 62: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 63: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 64: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 65: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 66: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 67: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 68: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 69: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 70: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 71: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 72: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 73: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 74: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 75: observed MAE=0.048876 rank=30\n","[SoftImpute] Iter 76: observed MAE=0.048877 rank=30\n","[SoftImpute] Iter 77: observed MAE=0.048877 rank=30\n","[SoftImpute] Iter 78: observed 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observed MAE=0.048881 rank=30\n","[SoftImpute] Iter 97: observed MAE=0.048881 rank=30\n","[SoftImpute] Iter 98: observed MAE=0.048881 rank=30\n","[SoftImpute] Iter 99: observed MAE=0.048881 rank=30\n","[SoftImpute] Iter 100: observed MAE=0.048881 rank=30\n","[SoftImpute] Stopped after iteration 100 for lambda=0.968362\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 101874\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 63400, constraints m = 80744\n","Cones:\tprimal zero / dual free vars: 8672\n","\tlinear vars: 26016\n","\tsd vars: 46056, sd blks: 1\n","Setup time: 8.28e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.14e+21  3.03e+21  1.00e+00 -1.53e+24  3.20e+23  5.13e+23  6.05e-02 \n","   100| 1.03e-03  1.38e-03  1.07e-04  1.48e+02  1.48e+02  5.32e-14  8.85e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.85e+00s\n","\tLin-sys: nnz in L factor: 252247, avg solve time: 1.62e-03s\n","\tCones: avg projection time: 6.03e-02s\n","\tAcceleration: avg step time: 2.20e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.3885e-09, dist(y, K*) = 1.4422e-09, s'y/|s||y| = -4.9222e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.8584e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.0034e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.1219e-04\n","----------------------------------------------------------------------------\n","c'x = 147.5804, -b'y = 147.5176\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 48.422582\n","[SoftImpute] Iter 1: observed MAE=0.048045 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.048351 rank=31\n","[SoftImpute] Iter 3: observed MAE=0.048506 rank=31\n","[SoftImpute] Iter 4: observed MAE=0.048619 rank=31\n","[SoftImpute] Iter 5: observed MAE=0.048699 rank=31\n","[SoftImpute] Iter 6: observed MAE=0.048759 rank=31\n","[SoftImpute] Iter 7: observed MAE=0.048803 rank=31\n","[SoftImpute] Iter 8: observed MAE=0.048834 rank=31\n","[SoftImpute] Iter 9: observed MAE=0.048856 rank=31\n","[SoftImpute] Iter 10: observed MAE=0.048872 rank=31\n","[SoftImpute] Iter 11: observed 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rank=30\n","[SoftImpute] Iter 65: observed MAE=0.048759 rank=30\n","[SoftImpute] Iter 66: observed MAE=0.048758 rank=30\n","[SoftImpute] Iter 67: observed MAE=0.048757 rank=30\n","[SoftImpute] Iter 68: observed MAE=0.048756 rank=30\n","[SoftImpute] Iter 69: observed MAE=0.048755 rank=30\n","[SoftImpute] Iter 70: observed MAE=0.048755 rank=30\n","[SoftImpute] Iter 71: observed MAE=0.048754 rank=30\n","[SoftImpute] Iter 72: observed MAE=0.048754 rank=30\n","[SoftImpute] Iter 73: observed MAE=0.048753 rank=30\n","[SoftImpute] Iter 74: observed MAE=0.048752 rank=30\n","[SoftImpute] Iter 75: observed MAE=0.048752 rank=30\n","[SoftImpute] Iter 76: observed MAE=0.048751 rank=30\n","[SoftImpute] Iter 77: observed MAE=0.048751 rank=30\n","[SoftImpute] Iter 78: observed MAE=0.048750 rank=30\n","[SoftImpute] Iter 79: observed MAE=0.048750 rank=30\n","[SoftImpute] Iter 80: observed MAE=0.048749 rank=30\n","[SoftImpute] Iter 81: observed MAE=0.048749 rank=30\n","[SoftImpute] Iter 82: observed MAE=0.048748 rank=30\n","[SoftImpute] Iter 83: observed MAE=0.048748 rank=30\n","[SoftImpute] Iter 84: observed MAE=0.048748 rank=30\n","[SoftImpute] Iter 85: observed MAE=0.048747 rank=30\n","[SoftImpute] Iter 86: observed MAE=0.048747 rank=30\n","[SoftImpute] Iter 87: observed MAE=0.048746 rank=30\n","[SoftImpute] Iter 88: observed MAE=0.048746 rank=30\n","[SoftImpute] Iter 89: observed MAE=0.048745 rank=30\n","[SoftImpute] Iter 90: observed MAE=0.048745 rank=30\n","[SoftImpute] Iter 91: observed MAE=0.048744 rank=30\n","[SoftImpute] Iter 92: observed MAE=0.048744 rank=30\n","[SoftImpute] Iter 93: observed MAE=0.048744 rank=30\n","[SoftImpute] Iter 94: observed MAE=0.048743 rank=30\n","[SoftImpute] Iter 95: observed MAE=0.048743 rank=30\n","[SoftImpute] Iter 96: observed MAE=0.048743 rank=30\n","[SoftImpute] Iter 97: observed MAE=0.048742 rank=30\n","[SoftImpute] Iter 98: observed MAE=0.048742 rank=30\n","[SoftImpute] Iter 99: observed MAE=0.048742 rank=30\n","[SoftImpute] Iter 100: observed MAE=0.048741 rank=30\n","[SoftImpute] Stopped after iteration 100 for lambda=0.968452\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 110108\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 69792, constraints m = 88224\n","Cones:\tprimal zero / dual free vars: 9216\n","\tlinear vars: 27648\n","\tsd vars: 51360, sd blks: 1\n","Setup time: 9.14e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.32e+21  3.21e+21  1.00e+00 -1.68e+24  3.47e+23  5.49e+23  5.89e-02 \n","   100| 1.58e-03  1.43e-03  3.30e-04  1.49e+02  1.49e+02  5.94e-14  8.86e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.87e+00s\n","\tLin-sys: nnz in L factor: 274458, avg solve time: 1.79e-03s\n","\tCones: avg projection time: 5.85e-02s\n","\tAcceleration: avg step time: 2.35e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6271e-09, dist(y, K*) = 1.4404e-08, s'y/|s||y| = 6.2186e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.6996e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.2325e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.8901e-04\n","----------------------------------------------------------------------------\n","c'x = 148.8624, -b'y = 148.8059\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 48.890510\n","[SoftImpute] Iter 1: observed MAE=0.048277 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.048612 rank=31\n","[SoftImpute] Iter 3: observed MAE=0.048757 rank=31\n","[SoftImpute] Iter 4: observed MAE=0.048855 rank=31\n","[SoftImpute] Iter 5: observed MAE=0.048922 rank=31\n","[SoftImpute] Iter 6: observed MAE=0.048969 rank=31\n","[SoftImpute] Iter 7: observed MAE=0.049001 rank=31\n","[SoftImpute] Iter 8: observed MAE=0.049023 rank=31\n","[SoftImpute] Iter 9: observed MAE=0.049036 rank=30\n","[SoftImpute] Iter 10: observed MAE=0.049041 rank=30\n","[SoftImpute] Iter 11: observed MAE=0.049045 rank=30\n","[SoftImpute] Iter 12: observed MAE=0.049047 rank=30\n","[SoftImpute] Iter 13: observed MAE=0.049048 rank=30\n","[SoftImpute] Iter 14: observed MAE=0.049048 rank=30\n","[SoftImpute] Iter 15: observed MAE=0.049047 rank=30\n","[SoftImpute] Iter 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Iter 87: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 88: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 89: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 90: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 91: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 92: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 93: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 94: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 95: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 96: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 97: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 98: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 99: observed MAE=0.049005 rank=30\n","[SoftImpute] Iter 100: observed MAE=0.049005 rank=30\n","[SoftImpute] Stopped after iteration 100 for lambda=0.977810\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 110108\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 69792, constraints m = 88224\n","Cones:\tprimal zero / dual free vars: 9216\n","\tlinear vars: 27648\n","\tsd vars: 51360, sd blks: 1\n","Setup time: 9.23e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.32e+21  3.21e+21  1.00e+00 -1.69e+24  3.50e+23  5.54e+23  5.90e-02 \n","   100| 6.45e-04  1.37e-03  9.08e-05  1.50e+02  1.50e+02  4.28e-14  8.99e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.99e+00s\n","\tLin-sys: nnz in L factor: 274458, avg solve time: 1.79e-03s\n","\tCones: avg projection time: 5.91e-02s\n","\tAcceleration: avg step time: 2.41e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6653e-09, dist(y, K*) = 1.3997e-08, s'y/|s||y| = -2.0971e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.4950e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.9870e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.7764e-04\n","----------------------------------------------------------------------------\n","c'x = 150.3340, -b'y = 150.2805\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 48.467764\n","[SoftImpute] Iter 1: observed MAE=0.048512 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.048847 rank=32\n","[SoftImpute] Iter 3: observed 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observed MAE=0.049378 rank=31\n","[SoftImpute] Iter 93: observed MAE=0.049378 rank=31\n","[SoftImpute] Iter 94: observed MAE=0.049378 rank=31\n","[SoftImpute] Iter 95: observed MAE=0.049378 rank=31\n","[SoftImpute] Iter 96: observed MAE=0.049378 rank=31\n","[SoftImpute] Iter 97: observed MAE=0.049378 rank=31\n","[SoftImpute] Iter 98: observed MAE=0.049378 rank=31\n","[SoftImpute] Iter 99: observed MAE=0.049377 rank=31\n","[SoftImpute] Iter 100: observed MAE=0.049377 rank=31\n","[SoftImpute] Stopped after iteration 100 for lambda=0.969355\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 99091\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 61213, constraints m = 78173\n","Cones:\tprimal zero / dual free vars: 8480\n","\tlinear vars: 25440\n","\tsd vars: 44253, sd blks: 1\n","Setup time: 8.81e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.08e+21  2.97e+21  1.00e+00 -1.48e+24  3.10e+23  5.01e+23  5.38e-02 \n","   100| 1.70e-03  2.45e-03  9.79e-05  1.46e+02  1.46e+02  5.12e-14  8.36e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.37e+00s\n","\tLin-sys: nnz in L factor: 244696, avg solve time: 1.64e-03s\n","\tCones: avg projection time: 5.65e-02s\n","\tAcceleration: avg step time: 2.10e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.4918e-09, dist(y, K*) = 4.5652e-09, s'y/|s||y| = 2.4825e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.4579e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.7069e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.4138e-05\n","----------------------------------------------------------------------------\n","c'x = 146.4292, -b'y = 146.4333\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 48.485981\n","[SoftImpute] Iter 1: observed MAE=0.047435 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.047692 rank=31\n","[SoftImpute] Iter 3: observed MAE=0.047851 rank=31\n","[SoftImpute] Iter 4: observed MAE=0.047963 rank=31\n","[SoftImpute] Iter 5: observed MAE=0.048044 rank=31\n","[SoftImpute] Iter 6: observed MAE=0.048103 rank=31\n","[SoftImpute] Iter 7: observed MAE=0.048145 rank=31\n","[SoftImpute] Iter 8: observed MAE=0.048175 rank=31\n","[SoftImpute] Iter 9: observed MAE=0.048198 rank=31\n","[SoftImpute] Iter 10: observed MAE=0.048214 rank=31\n","[SoftImpute] Iter 11: observed MAE=0.048226 rank=31\n","[SoftImpute] Iter 12: observed MAE=0.048235 rank=31\n","[SoftImpute] Iter 13: observed MAE=0.048242 rank=31\n","[SoftImpute] Iter 14: observed MAE=0.048246 rank=31\n","[SoftImpute] Iter 15: observed MAE=0.048248 rank=31\n","[SoftImpute] Iter 16: observed MAE=0.048249 rank=31\n","[SoftImpute] Iter 17: observed MAE=0.048248 rank=31\n","[SoftImpute] Iter 18: observed MAE=0.048248 rank=31\n","[SoftImpute] Iter 19: observed MAE=0.048246 rank=31\n","[SoftImpute] Iter 20: observed MAE=0.048245 rank=31\n","[SoftImpute] Iter 21: observed MAE=0.048243 rank=30\n","[SoftImpute] Iter 22: observed MAE=0.048239 rank=30\n","[SoftImpute] Iter 23: observed MAE=0.048235 rank=30\n","[SoftImpute] Iter 24: observed MAE=0.048232 rank=30\n","[SoftImpute] Iter 25: observed 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rank=30\n","[SoftImpute] Iter 79: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 80: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 81: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 82: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 83: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 84: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 85: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 86: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 87: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 88: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 89: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 90: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 91: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 92: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 93: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 94: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 95: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 96: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 97: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 98: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 99: observed MAE=0.048228 rank=30\n","[SoftImpute] Iter 100: observed MAE=0.048228 rank=30\n","[SoftImpute] Stopped after iteration 100 for lambda=0.969720\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 112078\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 71338, constraints m = 90026\n","Cones:\tprimal zero / dual free vars: 9344\n","\tlinear vars: 28032\n","\tsd vars: 52650, sd blks: 1\n","Setup time: 9.92e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.36e+21  3.25e+21  1.00e+00 -1.71e+24  3.54e+23  5.57e+23  5.51e-02 \n","   100| 1.22e-03  1.73e-03  2.43e-04  1.48e+02  1.48e+02  1.31e-14  9.27e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 9.27e+00s\n","\tLin-sys: nnz in L factor: 279796, avg solve time: 1.90e-03s\n","\tCones: avg projection time: 6.16e-02s\n","\tAcceleration: avg step time: 2.41e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6726e-09, dist(y, K*) = 1.1210e-08, s'y/|s||y| = -5.0459e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.1149e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.9078e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.1432e-04\n","----------------------------------------------------------------------------\n","c'x = 147.6531, -b'y = 147.5600\n","============================================================================\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"QQ-r552TJRAI"},"source":["### 40%"]},{"cell_type":"code","metadata":{"id":"c4CFS3sKJQcM","executionInfo":{"status":"ok","timestamp":1595214575882,"user_tz":300,"elapsed":209556,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"d04d7d99-d9ca-4310-c011-6913e643af47","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(0)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),66,55,45],\n","                  [sum(ytrain==1),70,65,60]])\n","    p = np.array([11,12,15,32])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,2) for k in np.arange(5)]\n","res40 = np.mean(np.asarray(res), axis=0)\n","res40"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 43.760492\n","[SoftImpute] Iter 1: observed MAE=0.046555 rank=31\n","[SoftImpute] Iter 2: observed MAE=0.046805 rank=31\n","[SoftImpute] Iter 3: observed MAE=0.046981 rank=31\n","[SoftImpute] Iter 4: observed MAE=0.047104 rank=31\n","[SoftImpute] Iter 5: observed MAE=0.047178 rank=30\n","[SoftImpute] Iter 6: observed MAE=0.047197 rank=29\n","[SoftImpute] Iter 7: observed MAE=0.047200 rank=29\n","[SoftImpute] Iter 8: observed MAE=0.047210 rank=29\n","[SoftImpute] Iter 9: observed MAE=0.047221 rank=29\n","[SoftImpute] Iter 10: observed MAE=0.047231 rank=29\n","[SoftImpute] Iter 11: observed MAE=0.047238 rank=29\n","[SoftImpute] Iter 12: observed MAE=0.047243 rank=29\n","[SoftImpute] Iter 13: observed MAE=0.047247 rank=29\n","[SoftImpute] Iter 14: observed MAE=0.047250 rank=29\n","[SoftImpute] Iter 15: observed MAE=0.047250 rank=29\n","[SoftImpute] Iter 16: observed MAE=0.047249 rank=29\n","[SoftImpute] Iter 17: observed MAE=0.047246 rank=29\n","[SoftImpute] Iter 18: observed MAE=0.047244 rank=29\n","[SoftImpute] Iter 19: observed MAE=0.047241 rank=29\n","[SoftImpute] Iter 20: observed MAE=0.047238 rank=29\n","[SoftImpute] Iter 21: observed MAE=0.047234 rank=29\n","[SoftImpute] Iter 22: observed MAE=0.047230 rank=29\n","[SoftImpute] Iter 23: observed MAE=0.047227 rank=29\n","[SoftImpute] Iter 24: observed MAE=0.047223 rank=29\n","[SoftImpute] Iter 25: observed MAE=0.047219 rank=29\n","[SoftImpute] Iter 26: observed 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rank=29\n","[SoftImpute] Iter 80: observed MAE=0.047119 rank=29\n","[SoftImpute] Iter 81: observed MAE=0.047117 rank=29\n","[SoftImpute] Iter 82: observed MAE=0.047116 rank=29\n","[SoftImpute] Iter 83: observed MAE=0.047115 rank=29\n","[SoftImpute] Iter 84: observed MAE=0.047114 rank=29\n","[SoftImpute] Iter 85: observed MAE=0.047113 rank=29\n","[SoftImpute] Iter 86: observed MAE=0.047112 rank=29\n","[SoftImpute] Iter 87: observed MAE=0.047111 rank=29\n","[SoftImpute] Iter 88: observed MAE=0.047110 rank=29\n","[SoftImpute] Iter 89: observed MAE=0.047109 rank=29\n","[SoftImpute] Iter 90: observed MAE=0.047107 rank=29\n","[SoftImpute] Iter 91: observed MAE=0.047106 rank=29\n","[SoftImpute] Iter 92: observed MAE=0.047105 rank=29\n","[SoftImpute] Iter 93: observed MAE=0.047104 rank=29\n","[SoftImpute] Iter 94: observed MAE=0.047103 rank=29\n","[SoftImpute] Iter 95: observed MAE=0.047102 rank=29\n","[SoftImpute] Iter 96: observed MAE=0.047101 rank=29\n","[SoftImpute] Iter 97: observed MAE=0.047100 rank=29\n","[SoftImpute] Iter 98: observed MAE=0.047099 rank=29\n","[SoftImpute] Iter 99: observed MAE=0.047098 rank=29\n","[SoftImpute] Iter 100: observed MAE=0.047098 rank=29\n","[SoftImpute] Stopped after iteration 100 for lambda=0.875210\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 99940\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 63400, constraints m = 80744\n","Cones:\tprimal zero / dual free vars: 8672\n","\tlinear vars: 26016\n","\tsd vars: 46056, sd blks: 1\n","Setup time: 9.21e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.17e+21  3.07e+21  1.00e+00 -1.44e+24  3.01e+23  4.67e+23  5.28e-02 \n","   100| 7.67e-04  1.08e-03  3.06e-04  1.38e+02  1.38e+02  9.53e-15  8.76e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.77e+00s\n","\tLin-sys: nnz in L factor: 249346, avg solve time: 1.63e-03s\n","\tCones: avg projection time: 5.97e-02s\n","\tAcceleration: avg step time: 2.16e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.3786e-09, dist(y, K*) = 4.1633e-09, s'y/|s||y| = -1.5071e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.1618e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.9830e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.0330e-04\n","----------------------------------------------------------------------------\n","c'x = 138.0912, -b'y = 138.0072\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 44.373157\n","[SoftImpute] Iter 1: observed MAE=0.046939 rank=31\n","[SoftImpute] Iter 2: observed MAE=0.047080 rank=30\n","[SoftImpute] Iter 3: observed MAE=0.047136 rank=30\n","[SoftImpute] Iter 4: observed MAE=0.047201 rank=30\n","[SoftImpute] Iter 5: observed MAE=0.047255 rank=30\n","[SoftImpute] Iter 6: observed MAE=0.047298 rank=30\n","[SoftImpute] Iter 7: observed MAE=0.047305 rank=29\n","[SoftImpute] Iter 8: observed MAE=0.047311 rank=29\n","[SoftImpute] Iter 9: observed MAE=0.047317 rank=29\n","[SoftImpute] Iter 10: observed MAE=0.047322 rank=29\n","[SoftImpute] Iter 11: observed MAE=0.047326 rank=29\n","[SoftImpute] Iter 12: observed MAE=0.047329 rank=29\n","[SoftImpute] Iter 13: observed MAE=0.047330 rank=29\n","[SoftImpute] Iter 14: observed MAE=0.047331 rank=29\n","[SoftImpute] Iter 15: observed MAE=0.047332 rank=29\n","[SoftImpute] Iter 16: observed MAE=0.047331 rank=29\n","[SoftImpute] Iter 17: observed MAE=0.047330 rank=29\n","[SoftImpute] Iter 18: observed MAE=0.047328 rank=29\n","[SoftImpute] Iter 19: observed MAE=0.047325 rank=29\n","[SoftImpute] Iter 20: observed MAE=0.047322 rank=29\n","[SoftImpute] Iter 21: observed MAE=0.047319 rank=29\n","[SoftImpute] Iter 22: observed MAE=0.047315 rank=29\n","[SoftImpute] Iter 23: observed MAE=0.047311 rank=29\n","[SoftImpute] Iter 24: observed MAE=0.047306 rank=29\n","[SoftImpute] Iter 25: observed MAE=0.047302 rank=29\n","[SoftImpute] Iter 26: observed MAE=0.047298 rank=29\n","[SoftImpute] Iter 27: observed MAE=0.047294 rank=29\n","[SoftImpute] Iter 28: observed MAE=0.047290 rank=29\n","[SoftImpute] Iter 29: observed MAE=0.047286 rank=29\n","[SoftImpute] Iter 30: observed MAE=0.047282 rank=29\n","[SoftImpute] Iter 31: observed 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observed MAE=0.047229 rank=29\n","[SoftImpute] Iter 50: observed MAE=0.047227 rank=29\n","[SoftImpute] Iter 51: observed MAE=0.047225 rank=29\n","[SoftImpute] Iter 52: observed MAE=0.047223 rank=29\n","[SoftImpute] Iter 53: observed MAE=0.047221 rank=29\n","[SoftImpute] Iter 54: observed MAE=0.047219 rank=29\n","[SoftImpute] Iter 55: observed MAE=0.047217 rank=29\n","[SoftImpute] Iter 56: observed MAE=0.047215 rank=29\n","[SoftImpute] Iter 57: observed MAE=0.047213 rank=29\n","[SoftImpute] Iter 58: observed MAE=0.047212 rank=29\n","[SoftImpute] Iter 59: observed MAE=0.047210 rank=29\n","[SoftImpute] Iter 60: observed MAE=0.047209 rank=29\n","[SoftImpute] Iter 61: observed MAE=0.047207 rank=29\n","[SoftImpute] Iter 62: observed MAE=0.047206 rank=29\n","[SoftImpute] Iter 63: observed MAE=0.047204 rank=29\n","[SoftImpute] Iter 64: observed MAE=0.047203 rank=29\n","[SoftImpute] Iter 65: observed MAE=0.047202 rank=29\n","[SoftImpute] Iter 66: observed MAE=0.047200 rank=29\n","[SoftImpute] Iter 67: observed MAE=0.047199 rank=29\n","[SoftImpute] Iter 68: observed MAE=0.047198 rank=29\n","[SoftImpute] Iter 69: observed MAE=0.047196 rank=29\n","[SoftImpute] Iter 70: observed MAE=0.047195 rank=29\n","[SoftImpute] Iter 71: observed MAE=0.047194 rank=29\n","[SoftImpute] Iter 72: observed MAE=0.047193 rank=29\n","[SoftImpute] Iter 73: observed MAE=0.047191 rank=29\n","[SoftImpute] Iter 74: observed MAE=0.047190 rank=29\n","[SoftImpute] Iter 75: observed MAE=0.047189 rank=29\n","[SoftImpute] Iter 76: observed MAE=0.047188 rank=29\n","[SoftImpute] Iter 77: observed MAE=0.047187 rank=29\n","[SoftImpute] Iter 78: observed MAE=0.047186 rank=29\n","[SoftImpute] Iter 79: observed MAE=0.047185 rank=29\n","[SoftImpute] Iter 80: observed MAE=0.047184 rank=29\n","[SoftImpute] Iter 81: observed MAE=0.047182 rank=29\n","[SoftImpute] Iter 82: observed MAE=0.047181 rank=29\n","[SoftImpute] Iter 83: observed MAE=0.047180 rank=29\n","[SoftImpute] Iter 84: observed MAE=0.047179 rank=29\n","[SoftImpute] Iter 85: observed MAE=0.047178 rank=29\n","[SoftImpute] Iter 86: observed MAE=0.047177 rank=29\n","[SoftImpute] Iter 87: observed MAE=0.047176 rank=29\n","[SoftImpute] Iter 88: observed MAE=0.047175 rank=29\n","[SoftImpute] Iter 89: observed MAE=0.047174 rank=29\n","[SoftImpute] Iter 90: observed MAE=0.047173 rank=29\n","[SoftImpute] Iter 91: observed MAE=0.047173 rank=29\n","[SoftImpute] Iter 92: observed MAE=0.047172 rank=29\n","[SoftImpute] Iter 93: observed MAE=0.047171 rank=29\n","[SoftImpute] Iter 94: observed MAE=0.047170 rank=29\n","[SoftImpute] Iter 95: observed MAE=0.047169 rank=29\n","[SoftImpute] Iter 96: observed MAE=0.047168 rank=29\n","[SoftImpute] Iter 97: observed MAE=0.047167 rank=29\n","[SoftImpute] Iter 98: observed MAE=0.047167 rank=29\n","[SoftImpute] Iter 99: observed MAE=0.047166 rank=29\n","[SoftImpute] Iter 100: observed MAE=0.047165 rank=29\n","[SoftImpute] Stopped after iteration 100 for lambda=0.887463\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 108338\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 69792, constraints m = 88224\n","Cones:\tprimal zero / dual free vars: 9216\n","\tlinear vars: 27648\n","\tsd vars: 51360, sd blks: 1\n","Setup time: 9.05e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.35e+21  3.23e+21  1.00e+00 -1.60e+24  3.31e+23  5.08e+23  5.03e-02 \n","   100| 8.54e-04  8.16e-04  1.68e-04  1.42e+02  1.42e+02  4.09e-14  8.86e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.86e+00s\n","\tLin-sys: nnz in L factor: 271803, avg solve time: 1.82e-03s\n","\tCones: avg projection time: 5.86e-02s\n","\tAcceleration: avg step time: 2.33e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.5818e-09, dist(y, K*) = 1.2843e-08, s'y/|s||y| = -8.3188e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.8104e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.3227e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.2538e-04\n","----------------------------------------------------------------------------\n","c'x = 142.1087, -b'y = 142.0729\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 44.666173\n","[SoftImpute] Iter 1: observed MAE=0.046864 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.047162 rank=31\n","[SoftImpute] Iter 3: observed MAE=0.047301 rank=31\n","[SoftImpute] Iter 4: observed MAE=0.047403 rank=31\n","[SoftImpute] Iter 5: observed MAE=0.047445 rank=30\n","[SoftImpute] Iter 6: observed MAE=0.047475 rank=30\n","[SoftImpute] Iter 7: observed MAE=0.047500 rank=30\n","[SoftImpute] Iter 8: observed MAE=0.047520 rank=30\n","[SoftImpute] Iter 9: observed MAE=0.047537 rank=30\n","[SoftImpute] Iter 10: observed MAE=0.047553 rank=30\n","[SoftImpute] Iter 11: observed MAE=0.047564 rank=29\n","[SoftImpute] Iter 12: observed MAE=0.047567 rank=29\n","[SoftImpute] Iter 13: observed MAE=0.047571 rank=29\n","[SoftImpute] Iter 14: observed MAE=0.047574 rank=29\n","[SoftImpute] Iter 15: observed MAE=0.047576 rank=29\n","[SoftImpute] Iter 16: observed MAE=0.047578 rank=29\n","[SoftImpute] Iter 17: observed MAE=0.047579 rank=29\n","[SoftImpute] 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rank=29\n","[SoftImpute] Iter 36: observed MAE=0.047565 rank=29\n","[SoftImpute] Iter 37: observed MAE=0.047563 rank=29\n","[SoftImpute] Iter 38: observed MAE=0.047562 rank=29\n","[SoftImpute] Iter 39: observed MAE=0.047561 rank=29\n","[SoftImpute] Iter 40: observed MAE=0.047560 rank=29\n","[SoftImpute] Iter 41: observed MAE=0.047558 rank=29\n","[SoftImpute] Iter 42: observed MAE=0.047557 rank=29\n","[SoftImpute] Iter 43: observed MAE=0.047556 rank=29\n","[SoftImpute] Iter 44: observed MAE=0.047555 rank=29\n","[SoftImpute] Iter 45: observed MAE=0.047554 rank=29\n","[SoftImpute] Iter 46: observed MAE=0.047552 rank=29\n","[SoftImpute] Iter 47: observed MAE=0.047551 rank=29\n","[SoftImpute] Iter 48: observed MAE=0.047550 rank=29\n","[SoftImpute] Iter 49: observed MAE=0.047549 rank=29\n","[SoftImpute] Iter 50: observed MAE=0.047548 rank=29\n","[SoftImpute] Iter 51: observed MAE=0.047547 rank=29\n","[SoftImpute] Iter 52: observed MAE=0.047547 rank=29\n","[SoftImpute] Iter 53: observed 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observed MAE=0.047530 rank=29\n","[SoftImpute] Iter 72: observed MAE=0.047529 rank=29\n","[SoftImpute] Iter 73: observed MAE=0.047528 rank=29\n","[SoftImpute] Iter 74: observed MAE=0.047527 rank=29\n","[SoftImpute] Iter 75: observed MAE=0.047526 rank=29\n","[SoftImpute] Iter 76: observed MAE=0.047525 rank=29\n","[SoftImpute] Iter 77: observed MAE=0.047524 rank=29\n","[SoftImpute] Iter 78: observed MAE=0.047523 rank=29\n","[SoftImpute] Iter 79: observed MAE=0.047522 rank=29\n","[SoftImpute] Iter 80: observed MAE=0.047521 rank=29\n","[SoftImpute] Iter 81: observed MAE=0.047520 rank=29\n","[SoftImpute] Iter 82: observed MAE=0.047518 rank=29\n","[SoftImpute] Iter 83: observed MAE=0.047517 rank=29\n","[SoftImpute] Iter 84: observed MAE=0.047516 rank=29\n","[SoftImpute] Iter 85: observed MAE=0.047515 rank=29\n","[SoftImpute] Iter 86: observed MAE=0.047514 rank=29\n","[SoftImpute] Iter 87: observed MAE=0.047513 rank=29\n","[SoftImpute] Iter 88: observed MAE=0.047512 rank=29\n","[SoftImpute] Iter 89: observed MAE=0.047511 rank=29\n","[SoftImpute] Iter 90: observed MAE=0.047510 rank=29\n","[SoftImpute] Iter 91: observed MAE=0.047509 rank=29\n","[SoftImpute] Iter 92: observed MAE=0.047508 rank=29\n","[SoftImpute] Iter 93: observed MAE=0.047507 rank=29\n","[SoftImpute] Iter 94: observed MAE=0.047506 rank=29\n","[SoftImpute] Iter 95: observed MAE=0.047505 rank=29\n","[SoftImpute] Iter 96: observed MAE=0.047504 rank=29\n","[SoftImpute] Iter 97: observed MAE=0.047503 rank=29\n","[SoftImpute] Iter 98: observed MAE=0.047502 rank=29\n","[SoftImpute] Iter 99: observed MAE=0.047501 rank=29\n","[SoftImpute] Iter 100: observed MAE=0.047500 rank=29\n","[SoftImpute] Stopped after iteration 100 for lambda=0.893323\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 108338\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 69792, constraints m = 88224\n","Cones:\tprimal zero / dual free vars: 9216\n","\tlinear vars: 27648\n","\tsd vars: 51360, sd blks: 1\n","Setup time: 9.36e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.35e+21  3.24e+21  1.00e+00 -1.61e+24  3.33e+23  5.10e+23  5.11e-02 \n","   100| 8.40e-04  1.14e-03  7.01e-05  1.42e+02  1.42e+02  8.93e-14  8.92e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.92e+00s\n","\tLin-sys: nnz in L factor: 271803, avg solve time: 1.82e-03s\n","\tCones: avg projection time: 5.91e-02s\n","\tAcceleration: avg step time: 2.35e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.4813e-09, dist(y, K*) = 3.1950e-08, s'y/|s||y| = 5.4417e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.4488e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 5.4681e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.9029e-05\n","----------------------------------------------------------------------------\n","c'x = 142.2875, -b'y = 142.2792\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 43.302097\n","[SoftImpute] Iter 1: observed MAE=0.047555 rank=32\n","[SoftImpute] Iter 2: observed MAE=0.047765 rank=31\n","[SoftImpute] Iter 3: observed MAE=0.047908 rank=31\n","[SoftImpute] Iter 4: observed MAE=0.048022 rank=31\n","[SoftImpute] Iter 5: observed MAE=0.048110 rank=31\n","[SoftImpute] Iter 6: observed MAE=0.048123 rank=30\n","[SoftImpute] Iter 7: observed MAE=0.048137 rank=30\n","[SoftImpute] Iter 8: observed MAE=0.048153 rank=30\n","[SoftImpute] Iter 9: observed MAE=0.048165 rank=30\n","[SoftImpute] Iter 10: observed MAE=0.048174 rank=30\n","[SoftImpute] Iter 11: observed MAE=0.048181 rank=30\n","[SoftImpute] Iter 12: observed MAE=0.048185 rank=30\n","[SoftImpute] Iter 13: observed MAE=0.048188 rank=30\n","[SoftImpute] Iter 14: observed MAE=0.048189 rank=30\n","[SoftImpute] Iter 15: observed MAE=0.048188 rank=30\n","[SoftImpute] Iter 16: observed MAE=0.048187 rank=30\n","[SoftImpute] Iter 17: observed MAE=0.048185 rank=30\n","[SoftImpute] Iter 18: observed MAE=0.048184 rank=30\n","[SoftImpute] Iter 19: observed MAE=0.048182 rank=30\n","[SoftImpute] Iter 20: observed MAE=0.048180 rank=30\n","[SoftImpute] Iter 21: observed MAE=0.048178 rank=30\n","[SoftImpute] Iter 22: observed MAE=0.048177 rank=30\n","[SoftImpute] Iter 23: observed 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rank=30\n","[SoftImpute] Iter 77: observed MAE=0.048107 rank=30\n","[SoftImpute] Iter 78: observed MAE=0.048106 rank=30\n","[SoftImpute] Iter 79: observed MAE=0.048105 rank=30\n","[SoftImpute] Iter 80: observed MAE=0.048104 rank=30\n","[SoftImpute] Iter 81: observed MAE=0.048103 rank=30\n","[SoftImpute] Iter 82: observed MAE=0.048102 rank=30\n","[SoftImpute] Iter 83: observed MAE=0.048101 rank=30\n","[SoftImpute] Iter 84: observed MAE=0.048100 rank=30\n","[SoftImpute] Iter 85: observed MAE=0.048100 rank=30\n","[SoftImpute] Iter 86: observed MAE=0.048099 rank=30\n","[SoftImpute] Iter 87: observed MAE=0.048098 rank=30\n","[SoftImpute] Iter 88: observed MAE=0.048097 rank=30\n","[SoftImpute] Iter 89: observed MAE=0.048096 rank=30\n","[SoftImpute] Iter 90: observed MAE=0.048095 rank=30\n","[SoftImpute] Iter 91: observed MAE=0.048094 rank=30\n","[SoftImpute] Iter 92: observed MAE=0.048094 rank=30\n","[SoftImpute] Iter 93: observed MAE=0.048093 rank=30\n","[SoftImpute] Iter 94: observed MAE=0.048092 rank=30\n","[SoftImpute] Iter 95: observed MAE=0.048091 rank=30\n","[SoftImpute] Iter 96: observed MAE=0.048091 rank=30\n","[SoftImpute] Iter 97: observed MAE=0.048090 rank=30\n","[SoftImpute] Iter 98: observed MAE=0.048089 rank=30\n","[SoftImpute] Iter 99: observed MAE=0.048088 rank=30\n","[SoftImpute] Iter 100: observed MAE=0.048088 rank=30\n","[SoftImpute] Stopped after iteration 100 for lambda=0.866042\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 97045\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 61213, constraints m = 78173\n","Cones:\tprimal zero / dual free vars: 8480\n","\tlinear vars: 25440\n","\tsd vars: 44253, sd blks: 1\n","Setup time: 8.24e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.11e+21  3.01e+21  1.00e+00 -1.39e+24  2.91e+23  4.53e+23  5.22e-02 \n","   100| 2.05e-03  2.36e-03  1.70e-04  1.40e+02  1.40e+02  9.38e-14  8.23e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.23e+00s\n","\tLin-sys: nnz in L factor: 241627, avg solve time: 1.61e-03s\n","\tCones: avg projection time: 5.57e-02s\n","\tAcceleration: avg step time: 2.06e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7166e-09, dist(y, K*) = 3.0518e-09, s'y/|s||y| = -3.7647e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.9609e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 5.2427e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.2359e-05\n","----------------------------------------------------------------------------\n","c'x = 139.4496, -b'y = 139.4434\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 44.611118\n","[SoftImpute] Iter 1: observed MAE=0.046188 rank=31\n","[SoftImpute] Iter 2: observed MAE=0.046386 rank=30\n","[SoftImpute] Iter 3: observed MAE=0.046465 rank=29\n","[SoftImpute] Iter 4: observed MAE=0.046498 rank=29\n","[SoftImpute] Iter 5: observed MAE=0.046539 rank=29\n","[SoftImpute] Iter 6: observed MAE=0.046574 rank=29\n","[SoftImpute] Iter 7: observed MAE=0.046602 rank=29\n","[SoftImpute] Iter 8: observed MAE=0.046624 rank=29\n","[SoftImpute] Iter 9: observed MAE=0.046643 rank=29\n","[SoftImpute] Iter 10: observed MAE=0.046658 rank=29\n","[SoftImpute] Iter 11: observed MAE=0.046669 rank=29\n","[SoftImpute] Iter 12: observed MAE=0.046678 rank=29\n","[SoftImpute] Iter 13: observed MAE=0.046682 rank=28\n","[SoftImpute] Iter 14: observed MAE=0.046683 rank=28\n","[SoftImpute] Iter 15: observed MAE=0.046685 rank=28\n","[SoftImpute] Iter 16: observed MAE=0.046687 rank=28\n","[SoftImpute] Iter 17: observed MAE=0.046689 rank=28\n","[SoftImpute] Iter 18: observed MAE=0.046691 rank=28\n","[SoftImpute] Iter 19: observed MAE=0.046691 rank=28\n","[SoftImpute] Iter 20: observed MAE=0.046692 rank=28\n","[SoftImpute] Iter 21: observed MAE=0.046692 rank=28\n","[SoftImpute] Iter 22: observed MAE=0.046692 rank=28\n","[SoftImpute] Iter 23: observed MAE=0.046691 rank=28\n","[SoftImpute] Iter 24: observed MAE=0.046690 rank=28\n","[SoftImpute] Iter 25: observed MAE=0.046689 rank=28\n","[SoftImpute] Iter 26: observed MAE=0.046687 rank=28\n","[SoftImpute] Iter 27: observed MAE=0.046686 rank=28\n","[SoftImpute] Iter 28: observed 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rank=28\n","[SoftImpute] Iter 82: observed MAE=0.046638 rank=28\n","[SoftImpute] Iter 83: observed MAE=0.046638 rank=28\n","[SoftImpute] Iter 84: observed MAE=0.046638 rank=28\n","[SoftImpute] Iter 85: observed MAE=0.046637 rank=28\n","[SoftImpute] Iter 86: observed MAE=0.046637 rank=28\n","[SoftImpute] Iter 87: observed MAE=0.046637 rank=28\n","[SoftImpute] Iter 88: observed MAE=0.046636 rank=28\n","[SoftImpute] Iter 89: observed MAE=0.046636 rank=28\n","[SoftImpute] Iter 90: observed MAE=0.046636 rank=28\n","[SoftImpute] Iter 91: observed MAE=0.046635 rank=28\n","[SoftImpute] Iter 92: observed MAE=0.046635 rank=28\n","[SoftImpute] Iter 93: observed MAE=0.046635 rank=28\n","[SoftImpute] Iter 94: observed MAE=0.046634 rank=28\n","[SoftImpute] Iter 95: observed MAE=0.046634 rank=28\n","[SoftImpute] Iter 96: observed MAE=0.046634 rank=28\n","[SoftImpute] Iter 97: observed MAE=0.046633 rank=28\n","[SoftImpute] Iter 98: observed MAE=0.046633 rank=28\n","[SoftImpute] Iter 99: observed MAE=0.046633 rank=28\n","[SoftImpute] Iter 100: observed MAE=0.046633 rank=28\n","[SoftImpute] Stopped after iteration 100 for lambda=0.892222\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 110356\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 71338, constraints m = 90026\n","Cones:\tprimal zero / dual free vars: 9344\n","\tlinear vars: 28032\n","\tsd vars: 52650, sd blks: 1\n","Setup time: 9.61e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.39e+21  3.28e+21  1.00e+00 -1.63e+24  3.37e+23  5.16e+23  5.83e-02 \n","   100| 3.51e-03  5.37e-03  3.07e-04  1.40e+02  1.39e+02  2.22e-14  9.44e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 9.45e+00s\n","\tLin-sys: nnz in L factor: 277213, avg solve time: 1.87e-03s\n","\tCones: avg projection time: 6.31e-02s\n","\tAcceleration: avg step time: 2.44e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.4936e-09, dist(y, K*) = 2.0479e-09, s'y/|s||y| = 9.7250e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.0932e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.6175e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 4.3175e-04\n","----------------------------------------------------------------------------\n","c'x = 139.4013, -b'y = 139.2805\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.15138467, 0.15297176, 0.16442566, 0.1695362 , 0.19133985,\n","       0.1645362 , 0.40202223])"]},"metadata":{"tags":[]},"execution_count":22}]},{"cell_type":"markdown","metadata":{"id":"g1BpljaMjHbc"},"source":["### 50%"]},{"cell_type":"code","metadata":{"id":"P7wRV2MrjKV3","executionInfo":{"status":"ok","timestamp":1604549251258,"user_tz":360,"elapsed":97901,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"9fc9e7be-ff3d-447d-ba7b-2188c2f9a920","colab":{"base_uri":"https://localhost:8080/"}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(0)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),60,55,45],\n","                  [sum(ytrain==1),60,55,45]])\n","    p = np.array([8,9,12,32])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,2) for k in np.arange(5)]\n","res50 = np.mean(np.asarray(res), axis=0)\n","res50"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 39.295570\n","[SoftImpute] Iter 1: observed MAE=0.046204 rank=31\n","[SoftImpute] Iter 2: observed MAE=0.046444 rank=31\n","[SoftImpute] Iter 3: observed MAE=0.046600 rank=30\n","[SoftImpute] Iter 4: observed MAE=0.046713 rank=30\n","[SoftImpute] Iter 5: observed MAE=0.046802 rank=30\n","[SoftImpute] Iter 6: observed MAE=0.046839 rank=29\n","[SoftImpute] Iter 7: observed MAE=0.046854 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rank=29\n","[SoftImpute] Iter 79: observed MAE=0.046796 rank=29\n","[SoftImpute] Iter 80: observed MAE=0.046796 rank=29\n","[SoftImpute] Iter 81: observed MAE=0.046795 rank=29\n","[SoftImpute] Iter 82: observed MAE=0.046794 rank=29\n","[SoftImpute] Iter 83: observed MAE=0.046794 rank=29\n","[SoftImpute] Iter 84: observed MAE=0.046793 rank=29\n","[SoftImpute] Iter 85: observed MAE=0.046793 rank=29\n","[SoftImpute] Iter 86: observed MAE=0.046792 rank=29\n","[SoftImpute] Iter 87: observed MAE=0.046792 rank=29\n","[SoftImpute] Iter 88: observed MAE=0.046791 rank=29\n","[SoftImpute] Iter 89: observed MAE=0.046791 rank=29\n","[SoftImpute] Iter 90: observed MAE=0.046790 rank=29\n","[SoftImpute] Iter 91: observed MAE=0.046790 rank=29\n","[SoftImpute] Iter 92: observed MAE=0.046789 rank=29\n","[SoftImpute] Iter 93: observed MAE=0.046789 rank=29\n","[SoftImpute] Iter 94: observed MAE=0.046788 rank=29\n","[SoftImpute] Iter 95: observed MAE=0.046788 rank=29\n","[SoftImpute] Iter 96: observed MAE=0.046787 rank=29\n","[SoftImpute] Iter 97: observed MAE=0.046787 rank=29\n","[SoftImpute] Iter 98: observed MAE=0.046786 rank=29\n","[SoftImpute] Iter 99: observed MAE=0.046786 rank=29\n","[SoftImpute] Iter 100: observed MAE=0.046785 rank=29\n","[SoftImpute] Stopped after iteration 100 for lambda=0.785911\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 98252\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 63400, constraints m = 80744\n","Cones:\tprimal zero / dual free vars: 8672\n","\tlinear vars: 26016\n","\tsd vars: 46056, sd blks: 1\n","Setup time: 7.45e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.20e+21  3.09e+21  1.00e+00 -1.34e+24  2.80e+23  4.21e+23  4.27e-02 \n","   100| 8.83e-04  1.46e-03  4.02e-05  1.31e+02  1.31e+02  9.70e-14  7.88e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 7.88e+00s\n","\tLin-sys: nnz in L factor: 246814, avg solve time: 1.81e-03s\n","\tCones: avg projection time: 5.22e-02s\n","\tAcceleration: avg step time: 1.98e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1998e-09, dist(y, K*) = 1.0110e-08, s'y/|s||y| = 6.8253e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.5744e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.3859e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.8764e-04\n","----------------------------------------------------------------------------\n","c'x = 130.9670, -b'y = 131.0163\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 39.612373\n","[SoftImpute] Iter 1: observed MAE=0.046494 rank=31\n","[SoftImpute] Iter 2: observed MAE=0.046631 rank=30\n","[SoftImpute] Iter 3: observed MAE=0.046734 rank=30\n","[SoftImpute] Iter 4: observed MAE=0.046817 rank=30\n","[SoftImpute] Iter 5: observed MAE=0.046876 rank=30\n","[SoftImpute] Iter 6: observed MAE=0.046893 rank=29\n","[SoftImpute] Iter 7: observed MAE=0.046907 rank=29\n","[SoftImpute] Iter 8: observed MAE=0.046919 rank=29\n","[SoftImpute] Iter 9: observed MAE=0.046927 rank=29\n","[SoftImpute] Iter 10: observed MAE=0.046932 rank=29\n","[SoftImpute] Iter 11: observed 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rank=29\n","[SoftImpute] Iter 65: observed MAE=0.046849 rank=29\n","[SoftImpute] Iter 66: observed MAE=0.046847 rank=29\n","[SoftImpute] Iter 67: observed MAE=0.046846 rank=29\n","[SoftImpute] Iter 68: observed MAE=0.046845 rank=29\n","[SoftImpute] Iter 69: observed MAE=0.046844 rank=29\n","[SoftImpute] Iter 70: observed MAE=0.046843 rank=29\n","[SoftImpute] Iter 71: observed MAE=0.046842 rank=29\n","[SoftImpute] Iter 72: observed MAE=0.046841 rank=29\n","[SoftImpute] Iter 73: observed MAE=0.046840 rank=29\n","[SoftImpute] Iter 74: observed MAE=0.046839 rank=29\n","[SoftImpute] Iter 75: observed MAE=0.046838 rank=29\n","[SoftImpute] Iter 76: observed MAE=0.046838 rank=29\n","[SoftImpute] Iter 77: observed MAE=0.046837 rank=29\n","[SoftImpute] Iter 78: observed MAE=0.046836 rank=29\n","[SoftImpute] Iter 79: observed MAE=0.046835 rank=29\n","[SoftImpute] Iter 80: observed MAE=0.046834 rank=29\n","[SoftImpute] Iter 81: observed MAE=0.046834 rank=29\n","[SoftImpute] Iter 82: observed MAE=0.046833 rank=29\n","[SoftImpute] Iter 83: observed MAE=0.046832 rank=29\n","[SoftImpute] Iter 84: observed MAE=0.046832 rank=29\n","[SoftImpute] Iter 85: observed MAE=0.046831 rank=29\n","[SoftImpute] Iter 86: observed MAE=0.046831 rank=29\n","[SoftImpute] Iter 87: observed MAE=0.046830 rank=29\n","[SoftImpute] Iter 88: observed MAE=0.046829 rank=29\n","[SoftImpute] Iter 89: observed MAE=0.046829 rank=29\n","[SoftImpute] Iter 90: observed MAE=0.046828 rank=29\n","[SoftImpute] Iter 91: observed MAE=0.046828 rank=29\n","[SoftImpute] Iter 92: observed MAE=0.046827 rank=29\n","[SoftImpute] Iter 93: observed MAE=0.046827 rank=29\n","[SoftImpute] Iter 94: observed MAE=0.046827 rank=29\n","[SoftImpute] Iter 95: observed MAE=0.046826 rank=29\n","[SoftImpute] Iter 96: observed MAE=0.046826 rank=29\n","[SoftImpute] Iter 97: observed MAE=0.046825 rank=29\n","[SoftImpute] Iter 98: observed MAE=0.046825 rank=29\n","[SoftImpute] Iter 99: observed MAE=0.046824 rank=29\n","[SoftImpute] Iter 100: observed MAE=0.046824 rank=29\n","[SoftImpute] Stopped after iteration 100 for lambda=0.792247\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 106548\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 69792, constraints m = 88224\n","Cones:\tprimal zero / dual free vars: 9216\n","\tlinear vars: 27648\n","\tsd vars: 51360, sd blks: 1\n","Setup time: 8.59e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.37e+21  3.26e+21  1.00e+00 -1.48e+24  3.07e+23  4.55e+23  4.44e-02 \n","   100| 4.17e-02  6.68e-02  7.51e-03  1.34e+02  1.32e+02  4.17e-14  8.25e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.26e+00s\n","\tLin-sys: nnz in L factor: 269118, avg solve time: 2.00e-03s\n","\tCones: avg projection time: 5.38e-02s\n","\tAcceleration: avg step time: 2.11e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.4115e-09, dist(y, K*) = 1.3311e-09, s'y/|s||y| = 5.1188e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.7702e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.6275e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.1574e-04\n","----------------------------------------------------------------------------\n","c'x = 134.2161, -b'y = 134.1311\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 39.974365\n","[SoftImpute] Iter 1: observed MAE=0.046398 rank=31\n","[SoftImpute] Iter 2: observed MAE=0.046607 rank=30\n","[SoftImpute] Iter 3: observed MAE=0.046718 rank=30\n","[SoftImpute] Iter 4: observed MAE=0.046804 rank=30\n","[SoftImpute] Iter 5: observed MAE=0.046865 rank=30\n","[SoftImpute] Iter 6: observed MAE=0.046897 rank=29\n","[SoftImpute] Iter 7: observed MAE=0.046901 rank=29\n","[SoftImpute] Iter 8: observed MAE=0.046906 rank=29\n","[SoftImpute] Iter 9: observed MAE=0.046909 rank=29\n","[SoftImpute] Iter 10: observed MAE=0.046908 rank=29\n","[SoftImpute] Iter 11: observed MAE=0.046905 rank=29\n","[SoftImpute] Iter 12: observed MAE=0.046902 rank=29\n","[SoftImpute] Iter 13: observed MAE=0.046898 rank=29\n","[SoftImpute] Iter 14: observed MAE=0.046893 rank=29\n","[SoftImpute] Iter 15: observed MAE=0.046887 rank=29\n","[SoftImpute] Iter 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rank=29\n","[SoftImpute] Iter 34: observed MAE=0.046785 rank=29\n","[SoftImpute] Iter 35: observed MAE=0.046782 rank=29\n","[SoftImpute] Iter 36: observed MAE=0.046779 rank=29\n","[SoftImpute] Iter 37: observed MAE=0.046777 rank=29\n","[SoftImpute] Iter 38: observed MAE=0.046774 rank=29\n","[SoftImpute] Iter 39: observed MAE=0.046772 rank=29\n","[SoftImpute] Iter 40: observed MAE=0.046770 rank=29\n","[SoftImpute] Iter 41: observed MAE=0.046768 rank=29\n","[SoftImpute] Iter 42: observed MAE=0.046766 rank=29\n","[SoftImpute] Iter 43: observed MAE=0.046764 rank=29\n","[SoftImpute] Iter 44: observed MAE=0.046762 rank=29\n","[SoftImpute] Iter 45: observed MAE=0.046760 rank=29\n","[SoftImpute] Iter 46: observed MAE=0.046759 rank=29\n","[SoftImpute] Iter 47: observed MAE=0.046757 rank=29\n","[SoftImpute] Iter 48: observed MAE=0.046755 rank=29\n","[SoftImpute] Iter 49: observed MAE=0.046753 rank=29\n","[SoftImpute] Iter 50: observed MAE=0.046751 rank=29\n","[SoftImpute] Iter 51: observed 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observed MAE=0.046726 rank=29\n","[SoftImpute] Iter 70: observed MAE=0.046725 rank=29\n","[SoftImpute] Iter 71: observed MAE=0.046724 rank=29\n","[SoftImpute] Iter 72: observed MAE=0.046723 rank=29\n","[SoftImpute] Iter 73: observed MAE=0.046722 rank=29\n","[SoftImpute] Iter 74: observed MAE=0.046721 rank=29\n","[SoftImpute] Iter 75: observed MAE=0.046720 rank=29\n","[SoftImpute] Iter 76: observed MAE=0.046719 rank=29\n","[SoftImpute] Iter 77: observed MAE=0.046718 rank=29\n","[SoftImpute] Iter 78: observed MAE=0.046717 rank=29\n","[SoftImpute] Iter 79: observed MAE=0.046716 rank=29\n","[SoftImpute] Iter 80: observed MAE=0.046715 rank=29\n","[SoftImpute] Iter 81: observed MAE=0.046714 rank=29\n","[SoftImpute] Iter 82: observed MAE=0.046713 rank=29\n","[SoftImpute] Iter 83: observed MAE=0.046712 rank=29\n","[SoftImpute] Iter 84: observed MAE=0.046712 rank=29\n","[SoftImpute] Iter 85: observed MAE=0.046711 rank=29\n","[SoftImpute] Iter 86: observed MAE=0.046710 rank=29\n","[SoftImpute] Iter 87: observed MAE=0.046709 rank=29\n","[SoftImpute] Iter 88: observed MAE=0.046708 rank=29\n","[SoftImpute] Iter 89: observed MAE=0.046707 rank=29\n","[SoftImpute] Iter 90: observed MAE=0.046707 rank=29\n","[SoftImpute] Iter 91: observed MAE=0.046706 rank=29\n","[SoftImpute] Iter 92: observed MAE=0.046705 rank=29\n","[SoftImpute] Iter 93: observed MAE=0.046705 rank=29\n","[SoftImpute] Iter 94: observed MAE=0.046704 rank=29\n","[SoftImpute] Iter 95: observed MAE=0.046703 rank=29\n","[SoftImpute] Iter 96: observed MAE=0.046703 rank=29\n","[SoftImpute] Iter 97: observed MAE=0.046702 rank=29\n","[SoftImpute] Iter 98: observed MAE=0.046701 rank=29\n","[SoftImpute] Iter 99: observed MAE=0.046701 rank=29\n","[SoftImpute] Iter 100: observed MAE=0.046700 rank=29\n","[SoftImpute] Stopped after iteration 100 for lambda=0.799487\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 106548\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 69792, constraints m = 88224\n","Cones:\tprimal zero / dual free vars: 9216\n","\tlinear vars: 27648\n","\tsd vars: 51360, sd blks: 1\n","Setup time: 8.34e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.37e+21  3.26e+21  1.00e+00 -1.49e+24  3.09e+23  4.59e+23  4.76e-02 \n","   100| 3.16e-03  5.00e-03  8.18e-05  1.34e+02  1.34e+02  9.65e-14  8.12e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.12e+00s\n","\tLin-sys: nnz in L factor: 269118, avg solve time: 1.96e-03s\n","\tCones: avg projection time: 5.28e-02s\n","\tAcceleration: avg step time: 2.11e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.5733e-09, dist(y, K*) = 2.5425e-09, s'y/|s||y| = 7.3579e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.1813e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.8197e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.3952e-04\n","----------------------------------------------------------------------------\n","c'x = 133.8366, -b'y = 133.8741\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 38.844818\n","[SoftImpute] Iter 1: observed MAE=0.046752 rank=31\n","[SoftImpute] Iter 2: observed MAE=0.046949 rank=31\n","[SoftImpute] Iter 3: observed MAE=0.047036 rank=30\n","[SoftImpute] Iter 4: observed MAE=0.047118 rank=30\n","[SoftImpute] Iter 5: observed MAE=0.047189 rank=30\n","[SoftImpute] Iter 6: observed MAE=0.047246 rank=30\n","[SoftImpute] Iter 7: observed MAE=0.047290 rank=30\n","[SoftImpute] Iter 8: observed MAE=0.047324 rank=30\n","[SoftImpute] Iter 9: observed MAE=0.047352 rank=30\n","[SoftImpute] Iter 10: observed MAE=0.047374 rank=30\n","[SoftImpute] Iter 11: observed MAE=0.047394 rank=30\n","[SoftImpute] Iter 12: observed MAE=0.047410 rank=30\n","[SoftImpute] Iter 13: observed MAE=0.047424 rank=30\n","[SoftImpute] Iter 14: observed MAE=0.047435 rank=30\n","[SoftImpute] Iter 15: observed MAE=0.047444 rank=30\n","[SoftImpute] Iter 16: observed MAE=0.047452 rank=30\n","[SoftImpute] Iter 17: observed MAE=0.047459 rank=30\n","[SoftImpute] Iter 18: observed MAE=0.047466 rank=30\n","[SoftImpute] Iter 19: observed MAE=0.047472 rank=30\n","[SoftImpute] Iter 20: observed MAE=0.047477 rank=30\n","[SoftImpute] Iter 21: 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rank=30\n","[SoftImpute] Iter 57: observed MAE=0.047529 rank=30\n","[SoftImpute] Iter 58: observed MAE=0.047529 rank=30\n","[SoftImpute] Iter 59: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 60: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 61: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 62: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 63: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 64: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 65: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 66: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 67: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 68: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 69: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 70: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 71: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 72: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 73: observed MAE=0.047530 rank=30\n","[SoftImpute] Iter 74: observed 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observed MAE=0.047528 rank=30\n","[SoftImpute] Iter 93: observed MAE=0.047528 rank=30\n","[SoftImpute] Iter 94: observed MAE=0.047528 rank=30\n","[SoftImpute] Iter 95: observed MAE=0.047528 rank=30\n","[SoftImpute] Iter 96: observed MAE=0.047528 rank=30\n","[SoftImpute] Iter 97: observed MAE=0.047528 rank=30\n","[SoftImpute] Iter 98: observed MAE=0.047528 rank=30\n","[SoftImpute] Iter 99: observed MAE=0.047528 rank=30\n","[SoftImpute] Iter 100: observed MAE=0.047528 rank=30\n","[SoftImpute] Stopped after iteration 100 for lambda=0.776896\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 95393\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 61213, constraints m = 78173\n","Cones:\tprimal zero / dual free vars: 8480\n","\tlinear vars: 25440\n","\tsd vars: 44253, sd blks: 1\n","Setup time: 7.73e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.14e+21  3.03e+21  1.00e+00 -1.29e+24  2.70e+23  4.08e+23  4.28e-02 \n","   100| 5.50e-03  9.28e-03  1.54e-04  1.31e+02  1.31e+02  2.06e-14  7.50e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 7.50e+00s\n","\tLin-sys: nnz in L factor: 239149, avg solve time: 1.77e-03s\n","\tCones: avg projection time: 4.93e-02s\n","\tAcceleration: avg step time: 1.92e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.2981e-09, dist(y, K*) = 5.3502e-09, s'y/|s||y| = -2.4449e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.4716e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 7.0731e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.0306e-04\n","----------------------------------------------------------------------------\n","c'x = 131.3566, -b'y = 131.3294\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 39.701522\n","[SoftImpute] Iter 1: observed MAE=0.045520 rank=30\n","[SoftImpute] Iter 2: observed MAE=0.045660 rank=30\n","[SoftImpute] Iter 3: observed MAE=0.045711 rank=29\n","[SoftImpute] Iter 4: observed MAE=0.045763 rank=29\n","[SoftImpute] Iter 5: observed MAE=0.045812 rank=29\n","[SoftImpute] Iter 6: observed MAE=0.045854 rank=29\n","[SoftImpute] Iter 7: observed MAE=0.045889 rank=29\n","[SoftImpute] Iter 8: observed MAE=0.045917 rank=29\n","[SoftImpute] Iter 9: observed MAE=0.045931 rank=28\n","[SoftImpute] Iter 10: observed MAE=0.045932 rank=28\n","[SoftImpute] Iter 11: observed MAE=0.045935 rank=28\n","[SoftImpute] Iter 12: observed MAE=0.045938 rank=28\n","[SoftImpute] Iter 13: observed MAE=0.045942 rank=28\n","[SoftImpute] Iter 14: observed MAE=0.045944 rank=28\n","[SoftImpute] Iter 15: observed MAE=0.045946 rank=28\n","[SoftImpute] Iter 16: observed MAE=0.045948 rank=28\n","[SoftImpute] Iter 17: observed MAE=0.045950 rank=28\n","[SoftImpute] Iter 18: observed MAE=0.045952 rank=28\n","[SoftImpute] Iter 19: observed MAE=0.045953 rank=28\n","[SoftImpute] Iter 20: observed MAE=0.045955 rank=28\n","[SoftImpute] Iter 21: observed MAE=0.045957 rank=28\n","[SoftImpute] Iter 22: observed MAE=0.045959 rank=28\n","[SoftImpute] Iter 23: observed MAE=0.045961 rank=28\n","[SoftImpute] Iter 24: observed MAE=0.045963 rank=28\n","[SoftImpute] Iter 25: observed 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observed MAE=0.045947 rank=27\n","[SoftImpute] Iter 44: observed MAE=0.045942 rank=27\n","[SoftImpute] Iter 45: observed MAE=0.045938 rank=27\n","[SoftImpute] Iter 46: observed MAE=0.045934 rank=27\n","[SoftImpute] Iter 47: observed MAE=0.045931 rank=27\n","[SoftImpute] Iter 48: observed MAE=0.045927 rank=27\n","[SoftImpute] Iter 49: observed MAE=0.045924 rank=27\n","[SoftImpute] Iter 50: observed MAE=0.045920 rank=27\n","[SoftImpute] Iter 51: observed MAE=0.045917 rank=27\n","[SoftImpute] Iter 52: observed MAE=0.045914 rank=27\n","[SoftImpute] Iter 53: observed MAE=0.045911 rank=27\n","[SoftImpute] Iter 54: observed MAE=0.045908 rank=27\n","[SoftImpute] Iter 55: observed MAE=0.045906 rank=27\n","[SoftImpute] Iter 56: observed MAE=0.045903 rank=27\n","[SoftImpute] Iter 57: observed MAE=0.045901 rank=27\n","[SoftImpute] Iter 58: observed MAE=0.045899 rank=27\n","[SoftImpute] Iter 59: observed MAE=0.045896 rank=27\n","[SoftImpute] Iter 60: observed MAE=0.045894 rank=27\n","[SoftImpute] Iter 61: observed MAE=0.045892 rank=27\n","[SoftImpute] Iter 62: observed MAE=0.045890 rank=27\n","[SoftImpute] Iter 63: observed MAE=0.045889 rank=27\n","[SoftImpute] Iter 64: observed MAE=0.045887 rank=27\n","[SoftImpute] Iter 65: observed MAE=0.045885 rank=27\n","[SoftImpute] Iter 66: observed MAE=0.045883 rank=27\n","[SoftImpute] Iter 67: observed MAE=0.045882 rank=27\n","[SoftImpute] Iter 68: observed MAE=0.045880 rank=27\n","[SoftImpute] Iter 69: observed MAE=0.045879 rank=27\n","[SoftImpute] Iter 70: observed MAE=0.045877 rank=27\n","[SoftImpute] Iter 71: observed MAE=0.045876 rank=27\n","[SoftImpute] Iter 72: observed MAE=0.045875 rank=27\n","[SoftImpute] Iter 73: observed MAE=0.045874 rank=27\n","[SoftImpute] Iter 74: observed MAE=0.045872 rank=27\n","[SoftImpute] Iter 75: observed MAE=0.045871 rank=27\n","[SoftImpute] Iter 76: observed MAE=0.045870 rank=27\n","[SoftImpute] Iter 77: observed MAE=0.045869 rank=27\n","[SoftImpute] Iter 78: observed MAE=0.045868 rank=27\n","[SoftImpute] Iter 79: observed MAE=0.045867 rank=27\n","[SoftImpute] Iter 80: observed MAE=0.045866 rank=27\n","[SoftImpute] Iter 81: observed MAE=0.045865 rank=27\n","[SoftImpute] Iter 82: observed MAE=0.045864 rank=27\n","[SoftImpute] Iter 83: observed MAE=0.045863 rank=27\n","[SoftImpute] Iter 84: observed MAE=0.045862 rank=27\n","[SoftImpute] Iter 85: observed MAE=0.045862 rank=27\n","[SoftImpute] Iter 86: observed MAE=0.045861 rank=27\n","[SoftImpute] Iter 87: observed MAE=0.045860 rank=27\n","[SoftImpute] Iter 88: observed MAE=0.045859 rank=27\n","[SoftImpute] Iter 89: observed MAE=0.045859 rank=27\n","[SoftImpute] Iter 90: observed MAE=0.045858 rank=27\n","[SoftImpute] Iter 91: observed MAE=0.045857 rank=27\n","[SoftImpute] Iter 92: observed MAE=0.045856 rank=27\n","[SoftImpute] Iter 93: observed MAE=0.045856 rank=27\n","[SoftImpute] Iter 94: observed MAE=0.045855 rank=27\n","[SoftImpute] Iter 95: observed MAE=0.045855 rank=27\n","[SoftImpute] Iter 96: observed MAE=0.045854 rank=27\n","[SoftImpute] Iter 97: observed MAE=0.045854 rank=27\n","[SoftImpute] Iter 98: observed MAE=0.045853 rank=27\n","[SoftImpute] Iter 99: observed MAE=0.045853 rank=27\n","[SoftImpute] Iter 100: observed MAE=0.045852 rank=27\n","[SoftImpute] Stopped after iteration 100 for lambda=0.794030\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 108542\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 71338, constraints m = 90026\n","Cones:\tprimal zero / dual free vars: 9344\n","\tlinear vars: 28032\n","\tsd vars: 52650, sd blks: 1\n","Setup time: 8.98e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 3.42e+21  3.30e+21  1.00e+00 -1.51e+24  3.11e+23  4.62e+23  5.39e-02 \n","   100| 1.55e-03  1.84e-03  4.39e-05  1.31e+02  1.31e+02  3.13e-14  8.82e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 8.82e+00s\n","\tLin-sys: nnz in L factor: 274492, avg solve time: 2.03e-03s\n","\tCones: avg projection time: 5.83e-02s\n","\tAcceleration: avg step time: 2.21e-02s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.4741e-09, dist(y, K*) = 1.2018e-09, s'y/|s||y| = -2.5464e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.5120e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.0019e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.2787e-04\n","----------------------------------------------------------------------------\n","c'x = 130.7896, -b'y = 130.7298\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.16403601, 0.16597195, 0.16107664, 0.16005945, 0.19447365,\n","       0.16827487, 0.49922732])"]},"metadata":{"tags":[]},"execution_count":13}]},{"cell_type":"markdown","metadata":{"id":"YszOfMjGKeu2"},"source":["### results"]},{"cell_type":"code","metadata":{"id":"l3z2uCDaKeBt","executionInfo":{"status":"ok","timestamp":1595216230757,"user_tz":300,"elapsed":1117,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"fbd3633e-e19e-4f25-9e57-c8b4932f561b","colab":{"base_uri":"https://localhost:8080/","height":118}},"source":["inosphere = np.vstack((res20,res30,res40))\n","inosphere"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[0.15535907, 0.15866975, 0.16091544, 0.15874908, 0.16866752,\n","        0.15874908, 0.20081745],\n","       [0.13938352, 0.1514952 , 0.13388334, 0.14573273, 0.15923935,\n","        0.14823273, 0.29875282],\n","       [0.15138467, 0.15297176, 0.16442566, 0.1695362 , 0.19133985,\n","        0.1645362 , 0.40202223]])"]},"metadata":{"tags":[]},"execution_count":26}]},{"cell_type":"markdown","metadata":{"id":"VGqInaaIIOOx"},"source":["## seeds "]},{"cell_type":"code","metadata":{"id":"_klPa7GkW_5V","executionInfo":{"status":"ok","timestamp":1604549393361,"user_tz":360,"elapsed":1047,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"232b05d0-ea17-488f-fa3a-0c271379e579","colab":{"base_uri":"https://localhost:8080/"}},"source":["data = pd.read_table('https://archive.ics.uci.edu/ml/machine-learning-databases/00236/seeds_dataset.txt',\n","                     sep = '\\s+', header = None)\n","print(data.head())\n","data = pd.DataFrame.to_numpy(data)\n","# reset the labels to go start from 0  \n","X,y = data[:,:7], data[:,7]-1 "],"execution_count":null,"outputs":[{"output_type":"stream","text":["       0      1       2      3      4      5      6  7\n","0  15.26  14.84  0.8710  5.763  3.312  2.221  5.220  1\n","1  14.88  14.57  0.8811  5.554  3.333  1.018  4.956  1\n","2  14.29  14.09  0.9050  5.291  3.337  2.699  4.825  1\n","3  13.84  13.94  0.8955  5.324  3.379  2.259  4.805  1\n","4  16.14  14.99  0.9034  5.658  3.562  1.355  5.175  1\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"_f-2AsWk5-mf","executionInfo":{"status":"ok","timestamp":1591370540328,"user_tz":300,"elapsed":16395,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"0ef5139e-37a9-4d47-dff7-4126299235f3","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(15)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    p = np.array([2,3,7])\n","    n = np.array([[sum(ytrain==0),50,40], [sum(ytrain==1),50,35],\n","                  [sum(ytrain==2),50,38]])    \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res20 = np.mean(np.asarray(res), axis=0)\n","res20"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 14.506631\n","[SoftImpute] Iter 1: observed MAE=0.018580 rank=6\n","[SoftImpute] Iter 2: observed MAE=0.018548 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.018533 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.018531 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018539 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018557 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018579 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018600 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018619 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018636 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018651 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018665 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018677 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018686 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018693 rank=6\n","[SoftImpute] Iter 16: observed MAE=0.018699 rank=6\n","[SoftImpute] Iter 17: observed MAE=0.018704 rank=6\n","[SoftImpute] Iter 18: observed MAE=0.018707 rank=6\n","[SoftImpute] Iter 19: observed MAE=0.018710 rank=6\n","[SoftImpute] Iter 20: observed MAE=0.018712 rank=6\n","[SoftImpute] Iter 21: observed MAE=0.018713 rank=6\n","[SoftImpute] Iter 22: observed MAE=0.018714 rank=6\n","[SoftImpute] Iter 23: observed MAE=0.018714 rank=6\n","[SoftImpute] Iter 24: observed MAE=0.018715 rank=6\n","[SoftImpute] Iter 25: observed MAE=0.018715 rank=6\n","[SoftImpute] Iter 26: observed MAE=0.018714 rank=6\n","[SoftImpute] Iter 27: observed MAE=0.018713 rank=6\n","[SoftImpute] Iter 28: observed MAE=0.018712 rank=6\n","[SoftImpute] Iter 29: observed MAE=0.018711 rank=6\n","[SoftImpute] Iter 30: observed MAE=0.018710 rank=6\n","[SoftImpute] Iter 31: observed MAE=0.018709 rank=6\n","[SoftImpute] Iter 32: observed MAE=0.018707 rank=6\n","[SoftImpute] Iter 33: observed MAE=0.018705 rank=6\n","[SoftImpute] Iter 34: observed MAE=0.018703 rank=6\n","[SoftImpute] Iter 35: observed MAE=0.018700 rank=6\n","[SoftImpute] Iter 36: observed MAE=0.018698 rank=6\n","[SoftImpute] Iter 37: observed MAE=0.018697 rank=6\n","[SoftImpute] Iter 38: observed MAE=0.018695 rank=6\n","[SoftImpute] Iter 39: observed MAE=0.018693 rank=6\n","[SoftImpute] Iter 40: observed MAE=0.018691 rank=6\n","[SoftImpute] Iter 41: observed MAE=0.018690 rank=6\n","[SoftImpute] Iter 42: observed MAE=0.018690 rank=6\n","[SoftImpute] Iter 43: observed MAE=0.018689 rank=6\n","[SoftImpute] Iter 44: observed MAE=0.018689 rank=6\n","[SoftImpute] Iter 45: observed MAE=0.018690 rank=6\n","[SoftImpute] Iter 46: observed MAE=0.018692 rank=6\n","[SoftImpute] Iter 47: observed MAE=0.018693 rank=6\n","[SoftImpute] Iter 48: observed MAE=0.018694 rank=6\n","[SoftImpute] Iter 49: observed MAE=0.018696 rank=6\n","[SoftImpute] Iter 50: observed MAE=0.018698 rank=6\n","[SoftImpute] Iter 51: observed MAE=0.018701 rank=6\n","[SoftImpute] Iter 52: observed MAE=0.018705 rank=6\n","[SoftImpute] Iter 53: observed MAE=0.018710 rank=6\n","[SoftImpute] Iter 54: observed MAE=0.018715 rank=6\n","[SoftImpute] Iter 55: observed MAE=0.018720 rank=6\n","[SoftImpute] Iter 56: observed MAE=0.018727 rank=6\n","[SoftImpute] Iter 57: observed MAE=0.018733 rank=6\n","[SoftImpute] Iter 58: observed MAE=0.018741 rank=6\n","[SoftImpute] Iter 59: observed MAE=0.018748 rank=6\n","[SoftImpute] Iter 60: observed MAE=0.018756 rank=6\n","[SoftImpute] Iter 61: observed MAE=0.018764 rank=6\n","[SoftImpute] Iter 62: observed MAE=0.018773 rank=6\n","[SoftImpute] Iter 63: observed MAE=0.018781 rank=6\n","[SoftImpute] Iter 64: observed MAE=0.018789 rank=6\n","[SoftImpute] Iter 65: observed MAE=0.018798 rank=6\n","[SoftImpute] Iter 66: observed MAE=0.018806 rank=6\n","[SoftImpute] Iter 67: observed MAE=0.018815 rank=6\n","[SoftImpute] Iter 68: observed MAE=0.018825 rank=6\n","[SoftImpute] Iter 69: observed MAE=0.018835 rank=6\n","[SoftImpute] Iter 70: observed MAE=0.018845 rank=6\n","[SoftImpute] Iter 71: observed MAE=0.018854 rank=6\n","[SoftImpute] Iter 72: observed MAE=0.018863 rank=6\n","[SoftImpute] Iter 73: observed MAE=0.018871 rank=6\n","[SoftImpute] Iter 74: observed MAE=0.018879 rank=6\n","[SoftImpute] Iter 75: observed MAE=0.018886 rank=6\n","[SoftImpute] Iter 76: observed MAE=0.018893 rank=6\n","[SoftImpute] Iter 77: observed MAE=0.018900 rank=6\n","[SoftImpute] Iter 78: observed MAE=0.018906 rank=6\n","[SoftImpute] Iter 79: observed MAE=0.018912 rank=6\n","[SoftImpute] Iter 80: observed MAE=0.018918 rank=6\n","[SoftImpute] Iter 81: observed MAE=0.018923 rank=6\n","[SoftImpute] Iter 82: observed MAE=0.018929 rank=6\n","[SoftImpute] Iter 83: observed MAE=0.018934 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.018939 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.018943 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.018948 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018952 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018956 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018959 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018963 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018966 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018969 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018972 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018974 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018977 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018979 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018981 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018984 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018985 rank=6\n","[SoftImpute] Stopped after iteration 99 for lambda=0.290133\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22517\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17188, constraints m = 19498\n","Cones:\tprimal zero / dual free vars: 1155\n","\tlinear vars: 3465\n","\tsd vars: 14878, sd blks: 1\n","Setup time: 4.20e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.67e+21  1.55e+21  1.00e+00 -1.90e+23  3.56e+22  5.07e+22  3.65e-02 \n","   100| 8.71e-04  1.25e-03  8.60e-05  2.55e+01  2.55e+01  3.66e-15  2.23e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.23e+00s\n","\tLin-sys: nnz in L factor: 60135, avg solve time: 4.50e-04s\n","\tCones: avg projection time: 1.59e-02s\n","\tAcceleration: avg step time: 4.75e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1228e-09, dist(y, K*) = 2.3620e-09, s'y/|s||y| = -9.4284e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.1958e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 5.0469e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.4685e-04\n","----------------------------------------------------------------------------\n","c'x = 25.5065, -b'y = 25.4884\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.425792\n","[SoftImpute] Iter 1: observed MAE=0.017906 rank=6\n","[SoftImpute] Iter 2: observed MAE=0.017886 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.017877 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.017879 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.017892 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.017906 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.017924 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.017941 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.017959 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.017974 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.017986 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.017996 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018005 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018013 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018020 rank=6\n","[SoftImpute] Iter 16: observed MAE=0.018025 rank=6\n","[SoftImpute] Iter 17: observed MAE=0.018030 rank=6\n","[SoftImpute] Iter 18: observed MAE=0.018033 rank=6\n","[SoftImpute] Iter 19: observed MAE=0.018037 rank=6\n","[SoftImpute] Iter 20: observed MAE=0.018040 rank=6\n","[SoftImpute] Iter 21: observed MAE=0.018043 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rank=6\n","[SoftImpute] Iter 76: observed MAE=0.018302 rank=6\n","[SoftImpute] Iter 77: observed MAE=0.018310 rank=6\n","[SoftImpute] Iter 78: observed MAE=0.018317 rank=6\n","[SoftImpute] Iter 79: observed MAE=0.018324 rank=6\n","[SoftImpute] Iter 80: observed MAE=0.018330 rank=6\n","[SoftImpute] Iter 81: observed MAE=0.018336 rank=6\n","[SoftImpute] Iter 82: observed MAE=0.018341 rank=6\n","[SoftImpute] Iter 83: observed MAE=0.018347 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.018352 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.018356 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.018361 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018365 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018369 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018372 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018376 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018379 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018382 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018385 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018388 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018391 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018393 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018395 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018397 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018399 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018401 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.288516\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 24904\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 19300, constraints m = 21764\n","Cones:\tprimal zero / dual free vars: 1232\n","\tlinear vars: 3696\n","\tsd vars: 16836, sd blks: 1\n","Setup time: 2.65e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.78e+21  1.66e+21  1.00e+00 -2.08e+23  3.87e+22  5.42e+22  1.91e-02 \n","   100| 1.34e-03  1.28e-03  2.21e-06  2.53e+01  2.53e+01  2.57e-14  2.48e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.48e+00s\n","\tLin-sys: nnz in L factor: 66922, avg solve time: 4.97e-04s\n","\tCones: avg projection time: 1.79e-02s\n","\tAcceleration: avg step time: 5.07e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.3899e-09, dist(y, K*) = 2.0260e-09, s'y/|s||y| = -6.8718e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.8781e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.2658e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 5.1396e-05\n","----------------------------------------------------------------------------\n","c'x = 25.3034, -b'y = 25.3061\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.627810\n","[SoftImpute] Iter 1: observed MAE=0.018335 rank=6\n","[SoftImpute] Iter 2: observed MAE=0.018309 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.018295 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.018290 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018294 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018304 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018316 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018328 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018341 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018351 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rank=6\n","[SoftImpute] Iter 65: observed MAE=0.018589 rank=6\n","[SoftImpute] Iter 66: observed MAE=0.018598 rank=6\n","[SoftImpute] Iter 67: observed MAE=0.018608 rank=6\n","[SoftImpute] Iter 68: observed MAE=0.018617 rank=6\n","[SoftImpute] Iter 69: observed MAE=0.018626 rank=6\n","[SoftImpute] Iter 70: observed MAE=0.018634 rank=6\n","[SoftImpute] Iter 71: observed MAE=0.018643 rank=6\n","[SoftImpute] Iter 72: observed MAE=0.018651 rank=6\n","[SoftImpute] Iter 73: observed MAE=0.018658 rank=6\n","[SoftImpute] Iter 74: observed MAE=0.018665 rank=6\n","[SoftImpute] Iter 75: observed MAE=0.018672 rank=6\n","[SoftImpute] Iter 76: observed MAE=0.018678 rank=6\n","[SoftImpute] Iter 77: observed MAE=0.018683 rank=6\n","[SoftImpute] Iter 78: observed MAE=0.018688 rank=6\n","[SoftImpute] Iter 79: observed MAE=0.018693 rank=6\n","[SoftImpute] Iter 80: observed MAE=0.018698 rank=6\n","[SoftImpute] Iter 81: observed MAE=0.018702 rank=6\n","[SoftImpute] Iter 82: observed MAE=0.018705 rank=6\n","[SoftImpute] Iter 83: observed MAE=0.018709 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.018712 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.018715 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.018718 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018721 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018723 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018726 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018728 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018730 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018732 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018733 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018735 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018737 rank=6\n","[SoftImpute] Stopped after iteration 95 for lambda=0.292556\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23804\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 18325, constraints m = 20719\n","Cones:\tprimal zero / dual free vars: 1197\n","\tlinear vars: 3591\n","\tsd vars: 15931, sd blks: 1\n","Setup time: 2.51e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.73e+21  1.61e+21  1.00e+00 -2.01e+23  3.76e+22  5.30e+22  1.39e-02 \n","   100| 9.94e-04  1.47e-03  3.23e-04  2.54e+01  2.54e+01  6.95e-15  2.33e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.34e+00s\n","\tLin-sys: nnz in L factor: 63792, avg solve time: 4.81e-04s\n","\tCones: avg projection time: 1.65e-02s\n","\tAcceleration: avg step time: 5.10e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.5365e-09, dist(y, K*) = 1.5255e-09, s'y/|s||y| = -2.2045e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.1081e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.1546e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.4007e-04\n","----------------------------------------------------------------------------\n","c'x = 25.4319, -b'y = 25.4143\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.424556\n","[SoftImpute] Iter 1: observed MAE=0.018520 rank=6\n","[SoftImpute] Iter 2: observed MAE=0.018504 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.018484 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.018468 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018460 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018456 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018455 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018455 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018457 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018458 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018459 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018459 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018459 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018459 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018458 rank=6\n","[SoftImpute] Iter 16: observed MAE=0.018456 rank=6\n","[SoftImpute] Iter 17: observed MAE=0.018454 rank=6\n","[SoftImpute] Iter 18: observed MAE=0.018451 rank=6\n","[SoftImpute] Iter 19: observed MAE=0.018447 rank=6\n","[SoftImpute] Iter 20: observed MAE=0.018443 rank=6\n","[SoftImpute] Iter 21: observed MAE=0.018439 rank=6\n","[SoftImpute] Iter 22: observed MAE=0.018436 rank=6\n","[SoftImpute] Iter 23: observed MAE=0.018433 rank=6\n","[SoftImpute] Iter 24: observed MAE=0.018430 rank=6\n","[SoftImpute] Iter 25: observed MAE=0.018427 rank=6\n","[SoftImpute] Iter 26: observed MAE=0.018426 rank=6\n","[SoftImpute] Iter 27: observed MAE=0.018427 rank=6\n","[SoftImpute] Iter 28: observed MAE=0.018429 rank=6\n","[SoftImpute] Iter 29: observed MAE=0.018431 rank=6\n","[SoftImpute] Iter 30: observed MAE=0.018437 rank=6\n","[SoftImpute] Iter 31: observed MAE=0.018444 rank=6\n","[SoftImpute] Iter 32: observed MAE=0.018454 rank=6\n","[SoftImpute] Iter 33: observed MAE=0.018467 rank=6\n","[SoftImpute] Iter 34: observed MAE=0.018482 rank=6\n","[SoftImpute] Iter 35: observed MAE=0.018496 rank=6\n","[SoftImpute] Iter 36: observed MAE=0.018512 rank=6\n","[SoftImpute] Iter 37: observed MAE=0.018529 rank=6\n","[SoftImpute] Iter 38: observed MAE=0.018546 rank=6\n","[SoftImpute] Iter 39: observed MAE=0.018562 rank=6\n","[SoftImpute] Iter 40: observed MAE=0.018579 rank=6\n","[SoftImpute] Iter 41: observed MAE=0.018596 rank=6\n","[SoftImpute] Iter 42: observed MAE=0.018611 rank=6\n","[SoftImpute] Iter 43: observed MAE=0.018626 rank=6\n","[SoftImpute] Iter 44: observed MAE=0.018641 rank=6\n","[SoftImpute] Iter 45: observed MAE=0.018655 rank=6\n","[SoftImpute] Iter 46: observed MAE=0.018668 rank=6\n","[SoftImpute] Iter 47: observed MAE=0.018679 rank=6\n","[SoftImpute] Iter 48: observed MAE=0.018689 rank=6\n","[SoftImpute] Iter 49: observed MAE=0.018699 rank=6\n","[SoftImpute] Iter 50: observed MAE=0.018709 rank=6\n","[SoftImpute] Iter 51: observed MAE=0.018717 rank=6\n","[SoftImpute] Iter 52: observed MAE=0.018725 rank=6\n","[SoftImpute] Iter 53: observed MAE=0.018732 rank=6\n","[SoftImpute] Iter 54: observed MAE=0.018739 rank=6\n","[SoftImpute] Iter 55: observed MAE=0.018744 rank=6\n","[SoftImpute] Iter 56: observed MAE=0.018749 rank=6\n","[SoftImpute] Iter 57: observed MAE=0.018754 rank=6\n","[SoftImpute] Iter 58: observed MAE=0.018757 rank=6\n","[SoftImpute] Iter 59: observed MAE=0.018761 rank=6\n","[SoftImpute] Iter 60: observed MAE=0.018764 rank=6\n","[SoftImpute] Iter 61: observed MAE=0.018767 rank=6\n","[SoftImpute] Iter 62: observed MAE=0.018769 rank=6\n","[SoftImpute] Iter 63: observed MAE=0.018772 rank=6\n","[SoftImpute] Iter 64: observed MAE=0.018774 rank=6\n","[SoftImpute] Iter 65: observed MAE=0.018776 rank=6\n","[SoftImpute] Iter 66: observed MAE=0.018777 rank=6\n","[SoftImpute] Iter 67: observed MAE=0.018779 rank=6\n","[SoftImpute] Iter 68: observed MAE=0.018780 rank=6\n","[SoftImpute] Iter 69: observed MAE=0.018781 rank=6\n","[SoftImpute] Iter 70: observed MAE=0.018782 rank=6\n","[SoftImpute] Iter 71: observed MAE=0.018784 rank=6\n","[SoftImpute] Iter 72: observed MAE=0.018784 rank=6\n","[SoftImpute] Iter 73: observed MAE=0.018785 rank=6\n","[SoftImpute] Iter 74: observed MAE=0.018786 rank=6\n","[SoftImpute] Iter 75: observed MAE=0.018787 rank=6\n","[SoftImpute] Iter 76: observed MAE=0.018788 rank=6\n","[SoftImpute] Iter 77: observed MAE=0.018788 rank=6\n","[SoftImpute] Iter 78: observed MAE=0.018789 rank=6\n","[SoftImpute] Stopped after iteration 78 for lambda=0.288491\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22727\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17375, constraints m = 19699\n","Cones:\tprimal zero / dual free vars: 1162\n","\tlinear vars: 3486\n","\tsd vars: 15051, sd blks: 1\n","Setup time: 2.34e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.68e+21  1.56e+21  1.00e+00 -1.88e+23  3.52e+22  5.01e+22  1.67e-02 \n","   100| 5.09e-03  6.36e-03  3.71e-04  2.46e+01  2.46e+01  1.27e-14  2.28e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.28e+00s\n","\tLin-sys: nnz in L factor: 60734, avg solve time: 4.49e-04s\n","\tCones: avg projection time: 1.66e-02s\n","\tAcceleration: avg step time: 4.56e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2191e-09, dist(y, K*) = 8.0326e-09, s'y/|s||y| = 1.3160e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.5521e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.2067e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.0842e-04\n","----------------------------------------------------------------------------\n","c'x = 24.5838, -b'y = 24.5943\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.493111\n","[SoftImpute] Iter 1: observed MAE=0.018440 rank=6\n","[SoftImpute] Iter 2: observed MAE=0.018419 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.018412 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.018415 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018421 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018432 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018442 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018451 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018459 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018466 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018472 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018477 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018480 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018484 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018488 rank=6\n","[SoftImpute] Iter 16: observed MAE=0.018492 rank=6\n","[SoftImpute] Iter 17: observed MAE=0.018494 rank=6\n","[SoftImpute] Iter 18: observed MAE=0.018497 rank=6\n","[SoftImpute] Iter 19: observed MAE=0.018498 rank=6\n","[SoftImpute] Iter 20: observed MAE=0.018499 rank=6\n","[SoftImpute] Iter 21: observed MAE=0.018501 rank=6\n","[SoftImpute] Iter 22: observed MAE=0.018503 rank=6\n","[SoftImpute] Iter 23: observed MAE=0.018505 rank=6\n","[SoftImpute] Iter 24: observed MAE=0.018508 rank=6\n","[SoftImpute] Iter 25: observed MAE=0.018511 rank=6\n","[SoftImpute] Iter 26: observed MAE=0.018516 rank=6\n","[SoftImpute] Iter 27: observed MAE=0.018520 rank=6\n","[SoftImpute] Iter 28: observed MAE=0.018526 rank=6\n","[SoftImpute] Iter 29: observed MAE=0.018533 rank=6\n","[SoftImpute] Iter 30: observed MAE=0.018541 rank=6\n","[SoftImpute] Iter 31: observed MAE=0.018551 rank=6\n","[SoftImpute] Iter 32: observed MAE=0.018560 rank=6\n","[SoftImpute] Iter 33: observed MAE=0.018573 rank=6\n","[SoftImpute] Iter 34: observed MAE=0.018588 rank=6\n","[SoftImpute] Iter 35: observed MAE=0.018605 rank=6\n","[SoftImpute] Iter 36: observed MAE=0.018623 rank=6\n","[SoftImpute] Iter 37: observed MAE=0.018643 rank=6\n","[SoftImpute] Iter 38: observed MAE=0.018665 rank=6\n","[SoftImpute] Iter 39: observed MAE=0.018687 rank=6\n","[SoftImpute] Iter 40: observed MAE=0.018710 rank=6\n","[SoftImpute] Iter 41: observed MAE=0.018734 rank=6\n","[SoftImpute] Iter 42: observed MAE=0.018761 rank=6\n","[SoftImpute] Iter 43: observed MAE=0.018786 rank=6\n","[SoftImpute] Iter 44: observed MAE=0.018812 rank=6\n","[SoftImpute] Iter 45: observed MAE=0.018838 rank=6\n","[SoftImpute] Iter 46: observed MAE=0.018862 rank=6\n","[SoftImpute] Iter 47: observed MAE=0.018885 rank=6\n","[SoftImpute] Iter 48: observed MAE=0.018907 rank=6\n","[SoftImpute] Iter 49: observed MAE=0.018927 rank=6\n","[SoftImpute] Iter 50: observed MAE=0.018945 rank=6\n","[SoftImpute] Iter 51: observed MAE=0.018962 rank=6\n","[SoftImpute] Iter 52: observed MAE=0.018976 rank=6\n","[SoftImpute] Iter 53: observed MAE=0.018989 rank=6\n","[SoftImpute] Iter 54: observed MAE=0.019001 rank=6\n","[SoftImpute] Iter 55: observed MAE=0.019011 rank=6\n","[SoftImpute] Iter 56: observed MAE=0.019019 rank=6\n","[SoftImpute] Iter 57: observed MAE=0.019027 rank=6\n","[SoftImpute] Iter 58: observed MAE=0.019034 rank=6\n","[SoftImpute] Iter 59: observed MAE=0.019031 rank=5\n","[SoftImpute] Iter 60: observed MAE=0.019023 rank=5\n","[SoftImpute] Iter 61: observed MAE=0.019017 rank=5\n","[SoftImpute] Iter 62: observed MAE=0.019013 rank=5\n","[SoftImpute] Iter 63: observed MAE=0.019010 rank=5\n","[SoftImpute] Iter 64: observed MAE=0.019008 rank=5\n","[SoftImpute] Iter 65: observed MAE=0.019006 rank=5\n","[SoftImpute] Iter 66: observed MAE=0.019004 rank=5\n","[SoftImpute] Iter 67: observed MAE=0.019002 rank=5\n","[SoftImpute] Iter 68: observed MAE=0.019001 rank=5\n","[SoftImpute] Iter 69: observed MAE=0.019000 rank=5\n","[SoftImpute] Iter 70: observed MAE=0.018999 rank=5\n","[SoftImpute] Iter 71: observed MAE=0.018998 rank=5\n","[SoftImpute] Iter 72: observed MAE=0.018997 rank=5\n","[SoftImpute] Iter 73: observed MAE=0.018996 rank=5\n","[SoftImpute] Iter 74: observed MAE=0.018995 rank=5\n","[SoftImpute] Iter 75: observed MAE=0.018995 rank=5\n","[SoftImpute] Iter 76: observed MAE=0.018994 rank=5\n","[SoftImpute] Iter 77: observed MAE=0.018994 rank=5\n","[SoftImpute] Iter 78: observed MAE=0.018993 rank=5\n","[SoftImpute] Iter 79: observed MAE=0.018992 rank=5\n","[SoftImpute] Stopped after iteration 79 for lambda=0.289862\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 21887\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 16633, constraints m = 18901\n","Cones:\tprimal zero / dual free vars: 1134\n","\tlinear vars: 3402\n","\tsd vars: 14365, sd blks: 1\n","Setup time: 2.28e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.64e+21  1.52e+21  1.00e+00 -1.82e+23  3.42e+22  4.90e+22  1.73e-02 \n","   100| 9.83e-04  1.14e-03  3.74e-04  2.46e+01  2.45e+01  5.65e-15  2.16e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.16e+00s\n","\tLin-sys: nnz in L factor: 58347, avg solve time: 4.46e-04s\n","\tCones: avg projection time: 1.53e-02s\n","\tAcceleration: avg step time: 4.70e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3170e-09, dist(y, K*) = 1.6671e-08, s'y/|s||y| = 6.0928e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.2550e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.5467e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 7.0117e-04\n","----------------------------------------------------------------------------\n","c'x = 24.5714, -b'y = 24.5362\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.03373977, 0.050962  , 0.04235088, 0.0523999 , 0.0858347 ,\n","       0.0523999 , 0.20211604])"]},"metadata":{"tags":[]},"execution_count":7}]},{"cell_type":"markdown","metadata":{"id":"n-ntTticmDKn"},"source":["### 30%"]},{"cell_type":"code","metadata":{"id":"UC7uhpy8W_6U","executionInfo":{"status":"ok","timestamp":1591370555512,"user_tz":300,"elapsed":22663,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"51e2bf82-97e4-44b5-9a81-91e1a5b43ede","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(15)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    p = np.array([2,3,7])\n","    n = np.array([[sum(ytrain==0),40,30], [sum(ytrain==1),45,30],\n","                  [sum(ytrain==2),40,30]])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res30 = np.mean(np.asarray(res), axis=0)\n","res30"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 13.472783\n","[SoftImpute] Iter 1: observed MAE=0.018825 rank=6\n","[SoftImpute] Iter 2: observed MAE=0.018743 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.018692 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.018668 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018675 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018691 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018713 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018736 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018762 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018786 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018809 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018829 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018845 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018858 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018869 rank=6\n","[SoftImpute] Iter 16: observed 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MAE=0.018827 rank=6\n","[SoftImpute] Iter 71: observed MAE=0.018825 rank=6\n","[SoftImpute] Iter 72: observed MAE=0.018823 rank=6\n","[SoftImpute] Iter 73: observed MAE=0.018822 rank=6\n","[SoftImpute] Iter 74: observed MAE=0.018820 rank=6\n","[SoftImpute] Iter 75: observed MAE=0.018819 rank=6\n","[SoftImpute] Iter 76: observed MAE=0.018817 rank=6\n","[SoftImpute] Iter 77: observed MAE=0.018815 rank=6\n","[SoftImpute] Iter 78: observed MAE=0.018814 rank=6\n","[SoftImpute] Iter 79: observed MAE=0.018812 rank=6\n","[SoftImpute] Iter 80: observed MAE=0.018811 rank=6\n","[SoftImpute] Iter 81: observed MAE=0.018810 rank=6\n","[SoftImpute] Iter 82: observed MAE=0.018809 rank=6\n","[SoftImpute] Iter 83: observed MAE=0.018808 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.018807 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.018806 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.018806 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018805 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018805 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018805 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018804 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018804 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018804 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018804 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018804 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018803 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018803 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018803 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018803 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018803 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018803 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.269456\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22283\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17188, constraints m = 19498\n","Cones:\tprimal zero / dual free vars: 1155\n","\tlinear vars: 3465\n","\tsd vars: 14878, sd blks: 1\n","Setup time: 1.91e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.68e+21  1.56e+21  1.00e+00 -1.80e+23  3.37e+22  4.69e+22  1.40e-02 \n","   100| 1.44e-03  2.01e-03  1.05e-05  2.43e+01  2.43e+01  2.01e-14  2.19e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.19e+00s\n","\tLin-sys: nnz in L factor: 59784, avg solve time: 4.90e-04s\n","\tCones: avg projection time: 1.55e-02s\n","\tAcceleration: avg step time: 4.76e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.0707e-09, dist(y, K*) = 1.3123e-09, s'y/|s||y| = -3.5072e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.5669e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.8409e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 9.4406e-05\n","----------------------------------------------------------------------------\n","c'x = 24.3092, -b'y = 24.3139\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.377594\n","[SoftImpute] Iter 1: observed MAE=0.018116 rank=6\n","[SoftImpute] Iter 2: observed MAE=0.018073 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.018043 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.018022 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018009 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018014 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018030 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018049 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018068 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018086 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018102 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018117 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018131 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018143 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018154 rank=6\n","[SoftImpute] Iter 16: observed MAE=0.018163 rank=6\n","[SoftImpute] Iter 17: observed MAE=0.018170 rank=6\n","[SoftImpute] Iter 18: observed MAE=0.018177 rank=6\n","[SoftImpute] Iter 19: observed MAE=0.018183 rank=6\n","[SoftImpute] Iter 20: observed MAE=0.018187 rank=6\n","[SoftImpute] Iter 21: observed MAE=0.018191 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rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018170 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018171 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018171 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018171 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018171 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018171 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018171 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.267552\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 24670\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 19300, constraints m = 21764\n","Cones:\tprimal zero / dual free vars: 1232\n","\tlinear vars: 3696\n","\tsd vars: 16836, sd blks: 1\n","Setup time: 2.52e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.79e+21  1.66e+21  1.00e+00 -1.98e+23  3.69e+22  5.04e+22  1.74e-02 \n","   100| 1.34e-03  1.54e-03  1.27e-06  2.45e+01  2.45e+01  2.17e-14  2.44e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.44e+00s\n","\tLin-sys: nnz in L factor: 66571, avg solve time: 4.84e-04s\n","\tCones: avg projection time: 1.76e-02s\n","\tAcceleration: avg step time: 5.02e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.3820e-09, dist(y, K*) = 2.2197e-09, s'y/|s||y| = -2.0494e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.8041e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.6997e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.5362e-04\n","----------------------------------------------------------------------------\n","c'x = 24.5708, -b'y = 24.5631\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.594530\n","[SoftImpute] Iter 1: observed MAE=0.018580 rank=6\n","[SoftImpute] Iter 2: observed MAE=0.018532 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.018499 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.018474 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018455 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018441 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018432 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018429 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018428 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018428 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rank=6\n","[SoftImpute] Iter 83: observed MAE=0.018402 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.018402 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.018402 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.018402 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018402 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018401 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018401 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018401 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018401 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018401 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018401 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018401 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018401 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018401 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018402 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018402 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018403 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018403 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.271891\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23570\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 18325, constraints m = 20719\n","Cones:\tprimal zero / dual free vars: 1197\n","\tlinear vars: 3591\n","\tsd vars: 15931, sd blks: 1\n","Setup time: 2.60e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.74e+21  1.62e+21  1.00e+00 -1.91e+23  3.57e+22  4.92e+22  1.76e-02 \n","   100| 1.65e-03  2.29e-03  1.85e-04  2.45e+01  2.45e+01  9.01e-15  2.35e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.35e+00s\n","\tLin-sys: nnz in L factor: 63441, avg solve time: 4.64e-04s\n","\tCones: avg projection time: 1.68e-02s\n","\tAcceleration: avg step time: 5.04e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.4143e-09, dist(y, K*) = 1.6112e-09, s'y/|s||y| = 6.4921e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.9642e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.6955e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.9882e-04\n","----------------------------------------------------------------------------\n","c'x = 24.5044, -b'y = 24.5193\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.323345\n","[SoftImpute] Iter 1: observed MAE=0.018887 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.018896 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.018845 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.018801 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018760 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018723 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018695 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018677 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018664 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018655 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018649 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018645 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018643 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018641 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018639 rank=6\n","[SoftImpute] Iter 16: observed 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MAE=0.018628 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018631 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018633 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018636 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018638 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018641 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018643 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018645 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018647 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018649 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018651 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018653 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018655 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.266467\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22495\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17375, constraints m = 19699\n","Cones:\tprimal zero / dual free vars: 1162\n","\tlinear vars: 3486\n","\tsd vars: 15051, sd blks: 1\n","Setup time: 2.28e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.69e+21  1.57e+21  1.00e+00 -1.77e+23  3.33e+22  4.61e+22  1.72e-02 \n","   100| 8.19e-04  7.81e-04  2.07e-04  2.35e+01  2.35e+01  6.37e-15  2.31e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.32e+00s\n","\tLin-sys: nnz in L factor: 60386, avg solve time: 4.45e-04s\n","\tCones: avg projection time: 1.68e-02s\n","\tAcceleration: avg step time: 4.64e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1500e-09, dist(y, K*) = 3.0461e-09, s'y/|s||y| = -1.8601e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.7108e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.4499e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 5.1250e-04\n","----------------------------------------------------------------------------\n","c'x = 23.5064, -b'y = 23.4818\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.358993\n","[SoftImpute] Iter 1: observed MAE=0.018793 rank=6\n","[SoftImpute] Iter 2: observed MAE=0.018728 rank=6\n","[SoftImpute] Iter 3: observed MAE=0.018672 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.018633 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018606 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018588 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018576 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018573 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018573 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018574 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018577 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018580 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018583 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018586 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018589 rank=6\n","[SoftImpute] Iter 16: observed MAE=0.018591 rank=6\n","[SoftImpute] Iter 17: observed MAE=0.018594 rank=6\n","[SoftImpute] Iter 18: observed MAE=0.018596 rank=6\n","[SoftImpute] Iter 19: observed MAE=0.018598 rank=6\n","[SoftImpute] Iter 20: observed MAE=0.018599 rank=6\n","[SoftImpute] Iter 21: observed MAE=0.018601 rank=6\n","[SoftImpute] Iter 22: observed MAE=0.018602 rank=6\n","[SoftImpute] Iter 23: observed MAE=0.018603 rank=6\n","[SoftImpute] Iter 24: observed MAE=0.018603 rank=6\n","[SoftImpute] Iter 25: observed MAE=0.018603 rank=6\n","[SoftImpute] Iter 26: observed MAE=0.018603 rank=6\n","[SoftImpute] Iter 27: observed MAE=0.018603 rank=6\n","[SoftImpute] Iter 28: observed MAE=0.018602 rank=6\n","[SoftImpute] Iter 29: observed MAE=0.018601 rank=6\n","[SoftImpute] Iter 30: observed MAE=0.018600 rank=6\n","[SoftImpute] Iter 31: observed MAE=0.018599 rank=6\n","[SoftImpute] Iter 32: observed MAE=0.018597 rank=6\n","[SoftImpute] Iter 33: observed MAE=0.018596 rank=6\n","[SoftImpute] Iter 34: observed MAE=0.018594 rank=6\n","[SoftImpute] Iter 35: observed MAE=0.018592 rank=6\n","[SoftImpute] Iter 36: observed MAE=0.018590 rank=6\n","[SoftImpute] Iter 37: observed MAE=0.018589 rank=6\n","[SoftImpute] Iter 38: observed MAE=0.018587 rank=6\n","[SoftImpute] Iter 39: observed MAE=0.018585 rank=6\n","[SoftImpute] Iter 40: observed MAE=0.018584 rank=6\n","[SoftImpute] Iter 41: observed MAE=0.018582 rank=6\n","[SoftImpute] Iter 42: observed MAE=0.018581 rank=6\n","[SoftImpute] Iter 43: observed MAE=0.018580 rank=6\n","[SoftImpute] Iter 44: observed MAE=0.018579 rank=6\n","[SoftImpute] Iter 45: observed MAE=0.018579 rank=6\n","[SoftImpute] Iter 46: observed MAE=0.018578 rank=6\n","[SoftImpute] Iter 47: observed MAE=0.018578 rank=6\n","[SoftImpute] Iter 48: observed MAE=0.018579 rank=6\n","[SoftImpute] Iter 49: observed MAE=0.018580 rank=6\n","[SoftImpute] Iter 50: observed MAE=0.018581 rank=6\n","[SoftImpute] Iter 51: observed MAE=0.018582 rank=6\n","[SoftImpute] Iter 52: observed MAE=0.018583 rank=6\n","[SoftImpute] Iter 53: observed MAE=0.018585 rank=6\n","[SoftImpute] Iter 54: observed MAE=0.018588 rank=6\n","[SoftImpute] Iter 55: observed MAE=0.018590 rank=6\n","[SoftImpute] Iter 56: observed MAE=0.018593 rank=6\n","[SoftImpute] Iter 57: observed MAE=0.018595 rank=6\n","[SoftImpute] Iter 58: observed MAE=0.018598 rank=6\n","[SoftImpute] Iter 59: observed MAE=0.018601 rank=6\n","[SoftImpute] Iter 60: observed MAE=0.018606 rank=6\n","[SoftImpute] Iter 61: observed MAE=0.018611 rank=6\n","[SoftImpute] Iter 62: observed MAE=0.018616 rank=6\n","[SoftImpute] Iter 63: observed MAE=0.018622 rank=6\n","[SoftImpute] Iter 64: observed MAE=0.018628 rank=6\n","[SoftImpute] Iter 65: observed MAE=0.018634 rank=6\n","[SoftImpute] Iter 66: observed MAE=0.018641 rank=6\n","[SoftImpute] Iter 67: observed MAE=0.018647 rank=6\n","[SoftImpute] Iter 68: observed MAE=0.018654 rank=6\n","[SoftImpute] Iter 69: observed MAE=0.018661 rank=6\n","[SoftImpute] Iter 70: observed MAE=0.018668 rank=6\n","[SoftImpute] Iter 71: observed MAE=0.018675 rank=6\n","[SoftImpute] Iter 72: observed MAE=0.018682 rank=6\n","[SoftImpute] Iter 73: observed MAE=0.018691 rank=6\n","[SoftImpute] Iter 74: observed MAE=0.018699 rank=6\n","[SoftImpute] Iter 75: observed MAE=0.018707 rank=6\n","[SoftImpute] Iter 76: observed MAE=0.018716 rank=6\n","[SoftImpute] Iter 77: observed MAE=0.018724 rank=6\n","[SoftImpute] Iter 78: observed MAE=0.018733 rank=6\n","[SoftImpute] Iter 79: observed MAE=0.018741 rank=6\n","[SoftImpute] Iter 80: observed MAE=0.018750 rank=6\n","[SoftImpute] Iter 81: observed MAE=0.018758 rank=6\n","[SoftImpute] Iter 82: observed MAE=0.018766 rank=6\n","[SoftImpute] Iter 83: observed MAE=0.018774 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.018782 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.018790 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.018797 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018805 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018812 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018820 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018827 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018834 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018840 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018846 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018852 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018858 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018863 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018868 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018872 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018877 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018881 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.267180\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 21653\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 16633, constraints m = 18901\n","Cones:\tprimal zero / dual free vars: 1134\n","\tlinear vars: 3402\n","\tsd vars: 14365, sd blks: 1\n","Setup time: 2.25e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.65e+21  1.53e+21  1.00e+00 -1.72e+23  3.23e+22  4.50e+22  1.68e-02 \n","   100| 7.99e-04  9.38e-04  2.01e-04  2.35e+01  2.35e+01  3.95e-15  2.11e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.11e+00s\n","\tLin-sys: nnz in L factor: 57996, avg solve time: 4.27e-04s\n","\tCones: avg projection time: 1.51e-02s\n","\tAcceleration: avg step time: 4.39e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.4399e-09, dist(y, K*) = 1.9894e-09, s'y/|s||y| = 5.3342e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.4044e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.1549e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.3305e-04\n","----------------------------------------------------------------------------\n","c'x = 23.4556, -b'y = 23.4397\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.03790644, 0.05106301, 0.06244892, 0.06207356, 0.08555693,\n","       0.06207356, 0.30151866])"]},"metadata":{"tags":[]},"execution_count":8}]},{"cell_type":"markdown","metadata":{"id":"cwOIOqZDlxnd"},"source":["### 40%"]},{"cell_type":"code","metadata":{"id":"PUGTfFsTIOO0","executionInfo":{"status":"ok","timestamp":1591370571474,"user_tz":300,"elapsed":36065,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"505b1bc0-de82-4155-b9ed-35aed40178db","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(15)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),35,24], [sum(ytrain==1),35,22],\n","                  [sum(ytrain==2),35,21]])\n","    p = np.array([2,3,7])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res40 = np.mean(np.asarray(res), axis=0)\n","res40"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 12.247909\n","[SoftImpute] Iter 1: observed MAE=0.018835 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.018853 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.018874 rank=7\n","[SoftImpute] Iter 4: observed MAE=0.018819 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.018756 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.018714 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018692 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018685 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018686 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018688 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018694 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018708 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018722 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018737 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018750 rank=6\n","[SoftImpute] Iter 16: observed MAE=0.018761 rank=6\n","[SoftImpute] Iter 17: observed MAE=0.018771 rank=6\n","[SoftImpute] Iter 18: observed MAE=0.018780 rank=6\n","[SoftImpute] Iter 19: observed MAE=0.018788 rank=6\n","[SoftImpute] Iter 20: observed MAE=0.018796 rank=6\n","[SoftImpute] Iter 21: observed MAE=0.018802 rank=6\n","[SoftImpute] Iter 22: observed MAE=0.018808 rank=6\n","[SoftImpute] Iter 23: observed MAE=0.018813 rank=6\n","[SoftImpute] Iter 24: observed MAE=0.018818 rank=6\n","[SoftImpute] Iter 25: observed MAE=0.018822 rank=6\n","[SoftImpute] Iter 26: observed MAE=0.018826 rank=6\n","[SoftImpute] Iter 27: observed MAE=0.018829 rank=6\n","[SoftImpute] Iter 28: observed MAE=0.018832 rank=6\n","[SoftImpute] Iter 29: observed MAE=0.018835 rank=6\n","[SoftImpute] Iter 30: observed MAE=0.018838 rank=6\n","[SoftImpute] Iter 31: observed MAE=0.018840 rank=6\n","[SoftImpute] Iter 32: observed MAE=0.018843 rank=6\n","[SoftImpute] Iter 33: observed MAE=0.018845 rank=6\n","[SoftImpute] Iter 34: observed MAE=0.018846 rank=6\n","[SoftImpute] Iter 35: observed MAE=0.018848 rank=6\n","[SoftImpute] Iter 36: observed MAE=0.018849 rank=6\n","[SoftImpute] Iter 37: observed MAE=0.018851 rank=6\n","[SoftImpute] Iter 38: observed MAE=0.018852 rank=6\n","[SoftImpute] Iter 39: observed MAE=0.018852 rank=6\n","[SoftImpute] Iter 40: observed MAE=0.018853 rank=6\n","[SoftImpute] Iter 41: observed MAE=0.018853 rank=6\n","[SoftImpute] Iter 42: observed MAE=0.018854 rank=6\n","[SoftImpute] Iter 43: observed MAE=0.018854 rank=6\n","[SoftImpute] Iter 44: observed MAE=0.018854 rank=6\n","[SoftImpute] Iter 45: observed MAE=0.018854 rank=6\n","[SoftImpute] Iter 46: observed MAE=0.018855 rank=6\n","[SoftImpute] Iter 47: observed MAE=0.018855 rank=6\n","[SoftImpute] Iter 48: observed MAE=0.018855 rank=6\n","[SoftImpute] Iter 49: observed MAE=0.018855 rank=6\n","[SoftImpute] Iter 50: observed MAE=0.018856 rank=6\n","[SoftImpute] Iter 51: observed MAE=0.018856 rank=6\n","[SoftImpute] Iter 52: observed MAE=0.018856 rank=6\n","[SoftImpute] Iter 53: observed MAE=0.018855 rank=6\n","[SoftImpute] Iter 54: observed MAE=0.018855 rank=6\n","[SoftImpute] Iter 55: observed MAE=0.018855 rank=6\n","[SoftImpute] Iter 56: observed MAE=0.018854 rank=6\n","[SoftImpute] Iter 57: observed MAE=0.018854 rank=6\n","[SoftImpute] Iter 58: observed MAE=0.018853 rank=6\n","[SoftImpute] Iter 59: observed MAE=0.018853 rank=6\n","[SoftImpute] Iter 60: observed MAE=0.018852 rank=6\n","[SoftImpute] Iter 61: observed MAE=0.018852 rank=6\n","[SoftImpute] Iter 62: observed MAE=0.018851 rank=6\n","[SoftImpute] Iter 63: observed MAE=0.018851 rank=6\n","[SoftImpute] Iter 64: observed MAE=0.018850 rank=6\n","[SoftImpute] Iter 65: observed MAE=0.018850 rank=6\n","[SoftImpute] Iter 66: observed MAE=0.018849 rank=6\n","[SoftImpute] Iter 67: observed MAE=0.018848 rank=6\n","[SoftImpute] Iter 68: observed MAE=0.018848 rank=6\n","[SoftImpute] Iter 69: observed MAE=0.018847 rank=6\n","[SoftImpute] Iter 70: observed MAE=0.018846 rank=6\n","[SoftImpute] Iter 71: observed MAE=0.018845 rank=6\n","[SoftImpute] Iter 72: observed MAE=0.018844 rank=6\n","[SoftImpute] Iter 73: observed MAE=0.018843 rank=6\n","[SoftImpute] Iter 74: observed MAE=0.018842 rank=6\n","[SoftImpute] Iter 75: observed MAE=0.018841 rank=6\n","[SoftImpute] Iter 76: observed MAE=0.018841 rank=6\n","[SoftImpute] Iter 77: observed MAE=0.018840 rank=6\n","[SoftImpute] Iter 78: observed MAE=0.018839 rank=6\n","[SoftImpute] Iter 79: observed MAE=0.018838 rank=6\n","[SoftImpute] Iter 80: observed MAE=0.018838 rank=6\n","[SoftImpute] Iter 81: observed MAE=0.018837 rank=6\n","[SoftImpute] Iter 82: observed MAE=0.018836 rank=6\n","[SoftImpute] Iter 83: observed MAE=0.018835 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.018834 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.018833 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.018832 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018831 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018830 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018829 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018828 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018827 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018825 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018824 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018823 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018822 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018821 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018820 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018819 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018818 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018816 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.244958\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22059\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17188, constraints m = 19498\n","Cones:\tprimal zero / dual free vars: 1155\n","\tlinear vars: 3465\n","\tsd vars: 14878, sd blks: 1\n","Setup time: 2.40e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.68e+21  1.57e+21  1.00e+00 -1.68e+23  3.15e+22  4.28e+22  1.82e-02 \n","   100| 7.37e-04  9.91e-04  1.87e-04  2.32e+01  2.32e+01  2.68e-16  2.17e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.17e+00s\n","\tLin-sys: nnz in L factor: 59448, avg solve time: 4.32e-04s\n","\tCones: avg projection time: 1.54e-02s\n","\tAcceleration: avg step time: 4.66e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.9873e-09, dist(y, K*) = 2.6376e-09, s'y/|s||y| = -5.8468e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.8003e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.0481e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.3660e-04\n","----------------------------------------------------------------------------\n","c'x = 23.1658, -b'y = 23.1498\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 12.150772\n","[SoftImpute] Iter 1: observed MAE=0.018099 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.018111 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.018040 rank=6\n","[SoftImpute] Iter 4: observed MAE=0.017965 rank=6\n","[SoftImpute] Iter 5: observed MAE=0.017911 rank=6\n","[SoftImpute] Iter 6: observed MAE=0.017880 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.017865 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.017858 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.017857 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.017862 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.017873 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.017884 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.017896 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.017909 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.017921 rank=6\n","[SoftImpute] Iter 16: observed MAE=0.017931 rank=6\n","[SoftImpute] Iter 17: observed MAE=0.017941 rank=6\n","[SoftImpute] Iter 18: observed MAE=0.017950 rank=6\n","[SoftImpute] Iter 19: observed MAE=0.017958 rank=6\n","[SoftImpute] Iter 20: observed MAE=0.017964 rank=6\n","[SoftImpute] Iter 21: observed MAE=0.017970 rank=6\n","[SoftImpute] Iter 22: observed MAE=0.017975 rank=6\n","[SoftImpute] Iter 23: observed MAE=0.017980 rank=6\n","[SoftImpute] Iter 24: observed MAE=0.017984 rank=6\n","[SoftImpute] Iter 25: observed MAE=0.017988 rank=6\n","[SoftImpute] Iter 26: observed MAE=0.017992 rank=6\n","[SoftImpute] Iter 27: observed MAE=0.017997 rank=6\n","[SoftImpute] Iter 28: observed MAE=0.018001 rank=6\n","[SoftImpute] Iter 29: observed MAE=0.018004 rank=6\n","[SoftImpute] Iter 30: observed MAE=0.018007 rank=6\n","[SoftImpute] Iter 31: observed MAE=0.018010 rank=6\n","[SoftImpute] Iter 32: observed MAE=0.018013 rank=6\n","[SoftImpute] Iter 33: observed MAE=0.018016 rank=6\n","[SoftImpute] Iter 34: observed MAE=0.018018 rank=6\n","[SoftImpute] Iter 35: observed MAE=0.018020 rank=6\n","[SoftImpute] Iter 36: observed MAE=0.018022 rank=6\n","[SoftImpute] Iter 37: observed MAE=0.018024 rank=6\n","[SoftImpute] Iter 38: observed MAE=0.018026 rank=6\n","[SoftImpute] Iter 39: observed MAE=0.018028 rank=6\n","[SoftImpute] Iter 40: observed MAE=0.018029 rank=6\n","[SoftImpute] Iter 41: observed MAE=0.018031 rank=6\n","[SoftImpute] Iter 42: observed MAE=0.018032 rank=6\n","[SoftImpute] Iter 43: observed MAE=0.018033 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rank=6\n","[SoftImpute] Iter 80: observed MAE=0.018046 rank=6\n","[SoftImpute] Iter 81: observed MAE=0.018046 rank=6\n","[SoftImpute] Iter 82: observed MAE=0.018046 rank=6\n","[SoftImpute] Iter 83: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018047 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018047 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.243015\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 24446\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 19300, constraints m = 21764\n","Cones:\tprimal zero / dual free vars: 1232\n","\tlinear vars: 3696\n","\tsd vars: 16836, sd blks: 1\n","Setup time: 2.44e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.79e+21  1.67e+21  1.00e+00 -1.84e+23  3.44e+22  4.60e+22  1.93e-02 \n","   100| 1.11e-03  1.42e-03  3.66e-04  2.33e+01  2.33e+01  9.87e-15  2.47e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.47e+00s\n","\tLin-sys: nnz in L factor: 66235, avg solve time: 4.77e-04s\n","\tCones: avg projection time: 1.75e-02s\n","\tAcceleration: avg step time: 5.39e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.4731e-09, dist(y, K*) = 1.0551e-09, s'y/|s||y| = 9.5028e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.3746e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.1305e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.4644e-04\n","----------------------------------------------------------------------------\n","c'x = 23.3314, -b'y = 23.3245\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 12.259137\n","[SoftImpute] Iter 1: observed MAE=0.018430 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.018445 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.018460 rank=7\n","[SoftImpute] Iter 4: observed MAE=0.018478 rank=7\n","[SoftImpute] Iter 5: observed MAE=0.018495 rank=7\n","[SoftImpute] Iter 6: observed MAE=0.018503 rank=6\n","[SoftImpute] Iter 7: observed MAE=0.018438 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018385 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018341 rank=6\n","[SoftImpute] Iter 10: observed MAE=0.018310 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018286 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018272 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018262 rank=6\n","[SoftImpute] Iter 14: 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MAE=0.018270 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018268 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018267 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018266 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018265 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018264 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018263 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018262 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018261 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018260 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018258 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018257 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018256 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018255 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018254 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.245183\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23346\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 18325, constraints m = 20719\n","Cones:\tprimal zero / dual free vars: 1197\n","\tlinear vars: 3591\n","\tsd vars: 15931, sd blks: 1\n","Setup time: 2.25e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.74e+21  1.62e+21  1.00e+00 -1.77e+23  3.32e+22  4.47e+22  1.76e-02 \n","   100| 1.12e-03  1.41e-03  9.27e-05  2.33e+01  2.33e+01  1.16e-14  2.31e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.31e+00s\n","\tLin-sys: nnz in L factor: 63105, avg solve time: 4.76e-04s\n","\tCones: avg projection time: 1.65e-02s\n","\tAcceleration: avg step time: 4.84e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.5134e-09, dist(y, K*) = 1.4403e-09, s'y/|s||y| = -4.7773e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.1784e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.5224e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.4004e-04\n","----------------------------------------------------------------------------\n","c'x = 23.2553, -b'y = 23.2486\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 12.119338\n","[SoftImpute] Iter 1: observed MAE=0.018507 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.018527 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.018544 rank=7\n","[SoftImpute] Iter 4: observed MAE=0.018560 rank=7\n","[SoftImpute] Iter 5: observed MAE=0.018572 rank=7\n","[SoftImpute] Iter 6: observed MAE=0.018587 rank=7\n","[SoftImpute] Iter 7: observed MAE=0.018606 rank=7\n","[SoftImpute] Iter 8: observed MAE=0.018627 rank=7\n","[SoftImpute] Iter 9: observed MAE=0.018652 rank=7\n","[SoftImpute] Iter 10: observed MAE=0.018620 rank=6\n","[SoftImpute] Iter 11: observed MAE=0.018584 rank=6\n","[SoftImpute] Iter 12: observed MAE=0.018562 rank=6\n","[SoftImpute] Iter 13: observed MAE=0.018549 rank=6\n","[SoftImpute] Iter 14: observed MAE=0.018542 rank=6\n","[SoftImpute] Iter 15: observed MAE=0.018540 rank=6\n","[SoftImpute] Iter 16: observed MAE=0.018541 rank=6\n","[SoftImpute] Iter 17: observed MAE=0.018543 rank=6\n","[SoftImpute] Iter 18: observed MAE=0.018545 rank=6\n","[SoftImpute] Iter 19: observed MAE=0.018547 rank=6\n","[SoftImpute] Iter 20: observed MAE=0.018550 rank=6\n","[SoftImpute] Iter 21: observed 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MAE=0.018491 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018490 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018489 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018489 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018488 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018487 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018486 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018486 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.242387\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22271\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17375, constraints m = 19699\n","Cones:\tprimal zero / dual free vars: 1162\n","\tlinear vars: 3486\n","\tsd vars: 15051, sd blks: 1\n","Setup time: 2.32e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.69e+21  1.58e+21  1.00e+00 -1.66e+23  3.12e+22  4.22e+22  1.38e-02 \n","   100| 1.90e-03  2.69e-03  5.88e-07  2.26e+01  2.26e+01  4.77e-16  2.33e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.33e+00s\n","\tLin-sys: nnz in L factor: 60050, avg solve time: 4.42e-04s\n","\tCones: avg projection time: 1.70e-02s\n","\tAcceleration: avg step time: 4.70e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2754e-09, dist(y, K*) = 8.3741e-10, s'y/|s||y| = -1.8909e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.9367e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.5018e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.7264e-04\n","----------------------------------------------------------------------------\n","c'x = 22.5662, -b'y = 22.5536\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 12.136178\n","[SoftImpute] Iter 1: observed MAE=0.018563 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.018580 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.018594 rank=7\n","[SoftImpute] Iter 4: observed MAE=0.018610 rank=7\n","[SoftImpute] Iter 5: observed MAE=0.018630 rank=7\n","[SoftImpute] Iter 6: observed MAE=0.018657 rank=7\n","[SoftImpute] Iter 7: observed MAE=0.018619 rank=6\n","[SoftImpute] Iter 8: observed MAE=0.018581 rank=6\n","[SoftImpute] Iter 9: observed MAE=0.018559 rank=6\n","[SoftImpute] Iter 10: 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MAE=0.018572 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.242724\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 21429\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 16633, constraints m = 18901\n","Cones:\tprimal zero / dual free vars: 1134\n","\tlinear vars: 3402\n","\tsd vars: 14365, sd blks: 1\n","Setup time: 2.50e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.65e+21  1.54e+21  1.00e+00 -1.61e+23  3.02e+22  4.11e+22  1.86e-02 \n","   100| 2.27e-03  3.64e-03  1.60e-04  2.25e+01  2.25e+01  7.70e-15  2.13e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.13e+00s\n","\tLin-sys: nnz in L factor: 57660, avg solve time: 4.30e-04s\n","\tCones: avg projection time: 1.51e-02s\n","\tAcceleration: avg step time: 4.55e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.5143e-09, dist(y, K*) = 1.0167e-08, s'y/|s||y| = -8.3296e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.5059e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.9875e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 5.2890e-05\n","----------------------------------------------------------------------------\n","c'x = 22.5473, -b'y = 22.5497\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.03790644, 0.07133781, 0.07790393, 0.07383827, 0.09444582,\n","       0.06795592, 0.39683806])"]},"metadata":{"tags":[]},"execution_count":9}]},{"cell_type":"code","metadata":{"id":"WqUjowQ77IaE","executionInfo":{"status":"ok","timestamp":1591370571478,"user_tz":300,"elapsed":34261,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"4d4a9f77-08a3-414e-8fdd-8d5c66ce0bd2","colab":{"base_uri":"https://localhost:8080/","height":118}},"source":["seeds = np.vstack((res20,res30,res40))\n","seeds"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[0.03373977, 0.050962  , 0.04235088, 0.0523999 , 0.0858347 ,\n","        0.0523999 , 0.20211604],\n","       [0.03790644, 0.05106301, 0.06244892, 0.06207356, 0.08555693,\n","        0.06207356, 0.30151866],\n","       [0.03790644, 0.07133781, 0.07790393, 0.07383827, 0.09444582,\n","        0.06795592, 0.39683806]])"]},"metadata":{"tags":[]},"execution_count":10}]},{"cell_type":"markdown","metadata":{"id":"ZZs8_BNwmOoh"},"source":["### 50%"]},{"cell_type":"code","metadata":{"id":"374GlMs-mQUN","executionInfo":{"status":"ok","timestamp":1604549868342,"user_tz":360,"elapsed":17438,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"89b861b7-20b9-49ef-84ff-7d509904afce","colab":{"base_uri":"https://localhost:8080/"}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(15)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),20,18,15], [sum(ytrain==1),20,18,15],\n","                  [sum(ytrain==2),20,18,15]])\n","    p = np.array([2,3,4,7])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res50 = np.mean(np.asarray(res), axis=0)\n","res50"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 10.905903\n","[SoftImpute] Iter 1: observed MAE=0.017644 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.017708 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.017774 rank=7\n","[SoftImpute] Iter 4: observed MAE=0.017839 rank=7\n","[SoftImpute] Iter 5: observed MAE=0.017906 rank=7\n","[SoftImpute] Iter 6: observed MAE=0.017962 rank=7\n","[SoftImpute] Iter 7: observed MAE=0.018011 rank=7\n","[SoftImpute] Iter 8: observed MAE=0.018050 rank=7\n","[SoftImpute] Iter 9: observed MAE=0.018077 rank=7\n","[SoftImpute] Iter 10: observed 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MAE=0.018346 rank=7\n","[SoftImpute] Stopped after iteration 100 for lambda=0.218118\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 21811\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17188, constraints m = 19498\n","Cones:\tprimal zero / dual free vars: 1155\n","\tlinear vars: 3465\n","\tsd vars: 14878, sd blks: 1\n","Setup time: 2.23e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.68e+21  1.58e+21  1.00e+00 -1.54e+23  2.89e+22  3.82e+22  1.89e-02 \n","   100| 1.44e-03  2.25e-03  2.52e-04  2.16e+01  2.16e+01  8.82e-15  2.24e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.24e+00s\n","\tLin-sys: nnz in L factor: 59076, avg solve time: 4.43e-04s\n","\tCones: avg projection time: 1.57e-02s\n","\tAcceleration: avg step time: 4.92e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.0069e-09, dist(y, K*) = 1.2616e-09, s'y/|s||y| = -5.4970e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.2083e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.0562e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.5838e-04\n","----------------------------------------------------------------------------\n","c'x = 21.6566, -b'y = 21.6496\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 10.735139\n","[SoftImpute] Iter 1: observed MAE=0.016869 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.016942 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.017019 rank=7\n","[SoftImpute] Iter 4: observed MAE=0.017093 rank=7\n","[SoftImpute] Iter 5: observed MAE=0.017158 rank=7\n","[SoftImpute] Iter 6: observed MAE=0.017216 rank=7\n","[SoftImpute] Iter 7: observed MAE=0.017263 rank=7\n","[SoftImpute] Iter 8: observed MAE=0.017302 rank=7\n","[SoftImpute] Iter 9: observed MAE=0.017330 rank=7\n","[SoftImpute] Iter 10: observed MAE=0.017350 rank=7\n","[SoftImpute] Iter 11: observed MAE=0.017365 rank=7\n","[SoftImpute] Iter 12: observed MAE=0.017377 rank=7\n","[SoftImpute] Iter 13: observed MAE=0.017387 rank=7\n","[SoftImpute] Iter 14: observed MAE=0.017394 rank=7\n","[SoftImpute] Iter 15: observed MAE=0.017400 rank=7\n","[SoftImpute] Iter 16: observed 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MAE=0.017608 rank=7\n","[SoftImpute] Iter 89: observed MAE=0.017609 rank=7\n","[SoftImpute] Iter 90: observed MAE=0.017609 rank=7\n","[SoftImpute] Iter 91: observed MAE=0.017610 rank=7\n","[SoftImpute] Iter 92: observed MAE=0.017610 rank=7\n","[SoftImpute] Iter 93: observed MAE=0.017611 rank=7\n","[SoftImpute] Iter 94: observed MAE=0.017611 rank=7\n","[SoftImpute] Iter 95: observed MAE=0.017611 rank=7\n","[SoftImpute] Iter 96: observed MAE=0.017612 rank=7\n","[SoftImpute] Iter 97: observed MAE=0.017612 rank=7\n","[SoftImpute] Iter 98: observed MAE=0.017613 rank=7\n","[SoftImpute] Iter 99: observed MAE=0.017613 rank=7\n","[SoftImpute] Iter 100: observed MAE=0.017613 rank=7\n","[SoftImpute] Stopped after iteration 100 for lambda=0.214703\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 24198\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 19300, constraints m = 21764\n","Cones:\tprimal zero / dual free vars: 1232\n","\tlinear vars: 3696\n","\tsd vars: 16836, sd blks: 1\n","Setup time: 2.21e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.79e+21  1.68e+21  1.00e+00 -1.68e+23  3.14e+22  4.10e+22  1.75e-02 \n","   100| 1.14e-03  1.16e-03  2.24e-04  2.18e+01  2.18e+01  6.37e-15  2.49e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.49e+00s\n","\tLin-sys: nnz in L factor: 65863, avg solve time: 4.86e-04s\n","\tCones: avg projection time: 1.77e-02s\n","\tAcceleration: avg step time: 5.35e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.0538e-09, dist(y, K*) = 7.3119e-09, s'y/|s||y| = 1.7454e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.3532e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 5.2511e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.1376e-05\n","----------------------------------------------------------------------------\n","c'x = 21.7636, -b'y = 21.7641\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 10.774189\n","[SoftImpute] Iter 1: observed MAE=0.017331 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.017414 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.017497 rank=7\n","[SoftImpute] Iter 4: observed MAE=0.017566 rank=7\n","[SoftImpute] Iter 5: observed MAE=0.017618 rank=7\n","[SoftImpute] Iter 6: observed MAE=0.017659 rank=7\n","[SoftImpute] Iter 7: observed MAE=0.017690 rank=7\n","[SoftImpute] Iter 8: observed MAE=0.017713 rank=7\n","[SoftImpute] Iter 9: observed MAE=0.017732 rank=7\n","[SoftImpute] Iter 10: observed MAE=0.017748 rank=7\n","[SoftImpute] Iter 11: observed MAE=0.017763 rank=7\n","[SoftImpute] Iter 12: observed MAE=0.017775 rank=7\n","[SoftImpute] Iter 13: observed MAE=0.017790 rank=7\n","[SoftImpute] Iter 14: observed MAE=0.017802 rank=7\n","[SoftImpute] Iter 15: observed MAE=0.017818 rank=7\n","[SoftImpute] Iter 16: observed MAE=0.017837 rank=7\n","[SoftImpute] Iter 17: observed MAE=0.017856 rank=7\n","[SoftImpute] Iter 18: observed MAE=0.017873 rank=7\n","[SoftImpute] Iter 19: observed MAE=0.017887 rank=7\n","[SoftImpute] Iter 20: observed MAE=0.017900 rank=7\n","[SoftImpute] Iter 21: observed MAE=0.017910 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rank=7\n","[SoftImpute] Iter 76: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 77: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 78: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 79: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 80: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 81: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 82: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 83: observed MAE=0.018024 rank=7\n","[SoftImpute] Iter 84: observed MAE=0.018024 rank=7\n","[SoftImpute] Iter 85: observed MAE=0.018024 rank=7\n","[SoftImpute] Iter 86: observed MAE=0.018024 rank=7\n","[SoftImpute] Iter 87: observed MAE=0.018024 rank=7\n","[SoftImpute] Iter 88: observed MAE=0.018024 rank=7\n","[SoftImpute] Iter 89: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 90: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 91: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 92: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 93: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 94: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 95: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 96: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 97: observed MAE=0.018023 rank=7\n","[SoftImpute] Iter 98: observed MAE=0.018022 rank=7\n","[SoftImpute] Iter 99: observed MAE=0.018022 rank=7\n","[SoftImpute] Iter 100: observed MAE=0.018022 rank=7\n","[SoftImpute] Stopped after iteration 100 for lambda=0.215484\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23098\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 18325, constraints m = 20719\n","Cones:\tprimal zero / dual free vars: 1197\n","\tlinear vars: 3591\n","\tsd vars: 15931, sd blks: 1\n","Setup time: 2.39e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.74e+21  1.63e+21  1.00e+00 -1.61e+23  3.01e+22  3.94e+22  1.76e-02 \n","   100| 1.50e-03  2.09e-03  3.55e-04  2.15e+01  2.15e+01  2.24e-15  2.33e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.33e+00s\n","\tLin-sys: nnz in L factor: 62733, avg solve time: 4.69e-04s\n","\tCones: avg projection time: 1.64e-02s\n","\tAcceleration: avg step time: 5.09e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1190e-09, dist(y, K*) = 2.7462e-09, s'y/|s||y| = 3.5796e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.5708e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.6755e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.1357e-04\n","----------------------------------------------------------------------------\n","c'x = 21.4869, -b'y = 21.4732\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 10.602542\n","[SoftImpute] Iter 1: observed MAE=0.017199 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.017269 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.017334 rank=7\n","[SoftImpute] Iter 4: observed MAE=0.017391 rank=7\n","[SoftImpute] Iter 5: observed MAE=0.017440 rank=7\n","[SoftImpute] Iter 6: observed MAE=0.017480 rank=7\n","[SoftImpute] Iter 7: observed MAE=0.017511 rank=7\n","[SoftImpute] Iter 8: observed MAE=0.017536 rank=7\n","[SoftImpute] Iter 9: observed MAE=0.017560 rank=7\n","[SoftImpute] Iter 10: observed MAE=0.017582 rank=7\n","[SoftImpute] Iter 11: observed MAE=0.017602 rank=7\n","[SoftImpute] Iter 12: observed MAE=0.017619 rank=7\n","[SoftImpute] Iter 13: observed MAE=0.017634 rank=7\n","[SoftImpute] Iter 14: observed MAE=0.017649 rank=7\n","[SoftImpute] Iter 15: observed MAE=0.017663 rank=7\n","[SoftImpute] Iter 16: observed MAE=0.017678 rank=7\n","[SoftImpute] Iter 17: observed MAE=0.017693 rank=7\n","[SoftImpute] Iter 18: observed MAE=0.017706 rank=7\n","[SoftImpute] Iter 19: observed MAE=0.017721 rank=7\n","[SoftImpute] Iter 20: observed MAE=0.017740 rank=7\n","[SoftImpute] Iter 21: observed MAE=0.017757 rank=7\n","[SoftImpute] Iter 22: observed MAE=0.017775 rank=7\n","[SoftImpute] Iter 23: observed MAE=0.017792 rank=7\n","[SoftImpute] Iter 24: observed MAE=0.017806 rank=7\n","[SoftImpute] Iter 25: observed MAE=0.017821 rank=7\n","[SoftImpute] Iter 26: observed MAE=0.017834 rank=7\n","[SoftImpute] Iter 27: observed MAE=0.017845 rank=7\n","[SoftImpute] Iter 28: observed MAE=0.017855 rank=7\n","[SoftImpute] Iter 29: observed MAE=0.017865 rank=7\n","[SoftImpute] Iter 30: observed MAE=0.017873 rank=7\n","[SoftImpute] Iter 31: observed MAE=0.017880 rank=7\n","[SoftImpute] Iter 32: observed MAE=0.017886 rank=7\n","[SoftImpute] Iter 33: observed MAE=0.017891 rank=7\n","[SoftImpute] Iter 34: observed MAE=0.017895 rank=7\n","[SoftImpute] Iter 35: observed MAE=0.017899 rank=7\n","[SoftImpute] Iter 36: observed MAE=0.017903 rank=7\n","[SoftImpute] Iter 37: observed MAE=0.017906 rank=7\n","[SoftImpute] Iter 38: observed MAE=0.017909 rank=7\n","[SoftImpute] Iter 39: observed MAE=0.017911 rank=7\n","[SoftImpute] Iter 40: observed MAE=0.017913 rank=7\n","[SoftImpute] Iter 41: observed MAE=0.017914 rank=7\n","[SoftImpute] Iter 42: observed MAE=0.017914 rank=6\n","[SoftImpute] Iter 43: observed MAE=0.017914 rank=6\n","[SoftImpute] Iter 44: observed MAE=0.017914 rank=6\n","[SoftImpute] Iter 45: observed MAE=0.017914 rank=6\n","[SoftImpute] Iter 46: observed MAE=0.017914 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rank=6\n","[SoftImpute] Iter 65: observed MAE=0.017908 rank=6\n","[SoftImpute] Iter 66: observed MAE=0.017908 rank=6\n","[SoftImpute] Iter 67: observed MAE=0.017907 rank=6\n","[SoftImpute] Iter 68: observed MAE=0.017907 rank=6\n","[SoftImpute] Iter 69: observed MAE=0.017907 rank=6\n","[SoftImpute] Iter 70: observed MAE=0.017906 rank=6\n","[SoftImpute] Iter 71: observed MAE=0.017906 rank=6\n","[SoftImpute] Iter 72: observed MAE=0.017905 rank=6\n","[SoftImpute] Iter 73: observed MAE=0.017905 rank=6\n","[SoftImpute] Iter 74: observed MAE=0.017904 rank=6\n","[SoftImpute] Iter 75: observed MAE=0.017904 rank=6\n","[SoftImpute] Iter 76: observed MAE=0.017903 rank=6\n","[SoftImpute] Iter 77: observed MAE=0.017903 rank=6\n","[SoftImpute] Iter 78: observed MAE=0.017902 rank=6\n","[SoftImpute] Iter 79: observed MAE=0.017901 rank=6\n","[SoftImpute] Iter 80: observed MAE=0.017901 rank=6\n","[SoftImpute] Iter 81: observed MAE=0.017900 rank=6\n","[SoftImpute] Iter 82: observed MAE=0.017900 rank=6\n","[SoftImpute] Iter 83: observed MAE=0.017899 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.017898 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.017898 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.017897 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.017896 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.017896 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.017895 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.017895 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.017894 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.017894 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.017893 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.017893 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.017893 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.017892 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.017892 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.017892 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.017892 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.017891 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.212051\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22023\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17375, constraints m = 19699\n","Cones:\tprimal zero / dual free vars: 1162\n","\tlinear vars: 3486\n","\tsd vars: 15051, sd blks: 1\n","Setup time: 2.09e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.69e+21  1.58e+21  1.00e+00 -1.50e+23  2.82e+22  3.71e+22  1.21e-02 \n","   100| 1.28e-03  1.56e-03  1.80e-04  2.08e+01  2.08e+01  1.60e-14  2.32e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.32e+00s\n","\tLin-sys: nnz in L factor: 59678, avg solve time: 4.43e-04s\n","\tCones: avg projection time: 1.67e-02s\n","\tAcceleration: avg step time: 4.84e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2430e-09, dist(y, K*) = 4.1887e-09, s'y/|s||y| = 3.4964e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.8014e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.1008e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.4133e-04\n","----------------------------------------------------------------------------\n","c'x = 20.8247, -b'y = 20.8186\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 10.558315\n","[SoftImpute] Iter 1: observed MAE=0.017341 rank=7\n","[SoftImpute] Iter 2: observed MAE=0.017448 rank=7\n","[SoftImpute] Iter 3: observed MAE=0.017555 rank=7\n","[SoftImpute] Iter 4: observed MAE=0.017643 rank=7\n","[SoftImpute] Iter 5: observed MAE=0.017709 rank=7\n","[SoftImpute] Iter 6: observed MAE=0.017760 rank=7\n","[SoftImpute] Iter 7: observed MAE=0.017800 rank=7\n","[SoftImpute] Iter 8: observed MAE=0.017832 rank=7\n","[SoftImpute] Iter 9: observed MAE=0.017857 rank=7\n","[SoftImpute] Iter 10: observed MAE=0.017876 rank=7\n","[SoftImpute] Iter 11: observed MAE=0.017893 rank=7\n","[SoftImpute] Iter 12: observed MAE=0.017907 rank=7\n","[SoftImpute] Iter 13: observed MAE=0.017920 rank=7\n","[SoftImpute] Iter 14: observed MAE=0.017933 rank=7\n","[SoftImpute] Iter 15: observed MAE=0.017943 rank=7\n","[SoftImpute] Iter 16: observed MAE=0.017951 rank=7\n","[SoftImpute] Iter 17: observed MAE=0.017956 rank=7\n","[SoftImpute] Iter 18: observed MAE=0.017960 rank=7\n","[SoftImpute] Iter 19: observed MAE=0.017963 rank=7\n","[SoftImpute] Iter 20: observed MAE=0.017963 rank=7\n","[SoftImpute] Iter 21: observed MAE=0.017964 rank=7\n","[SoftImpute] Iter 22: observed MAE=0.017972 rank=7\n","[SoftImpute] Iter 23: observed MAE=0.017979 rank=7\n","[SoftImpute] Iter 24: observed MAE=0.017984 rank=7\n","[SoftImpute] Iter 25: observed MAE=0.017991 rank=7\n","[SoftImpute] Iter 26: observed MAE=0.018000 rank=7\n","[SoftImpute] Iter 27: observed MAE=0.018008 rank=7\n","[SoftImpute] Iter 28: observed MAE=0.018016 rank=7\n","[SoftImpute] Iter 29: observed MAE=0.018022 rank=7\n","[SoftImpute] Iter 30: observed MAE=0.018026 rank=7\n","[SoftImpute] Iter 31: observed MAE=0.018030 rank=7\n","[SoftImpute] Iter 32: observed MAE=0.018034 rank=7\n","[SoftImpute] Iter 33: observed MAE=0.018038 rank=7\n","[SoftImpute] Iter 34: observed 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MAE=0.018053 rank=7\n","[SoftImpute] Iter 53: observed MAE=0.018053 rank=7\n","[SoftImpute] Iter 54: observed MAE=0.018054 rank=7\n","[SoftImpute] Iter 55: observed MAE=0.018054 rank=7\n","[SoftImpute] Iter 56: observed MAE=0.018055 rank=7\n","[SoftImpute] Iter 57: observed MAE=0.018055 rank=7\n","[SoftImpute] Iter 58: observed MAE=0.018056 rank=7\n","[SoftImpute] Iter 59: observed MAE=0.018057 rank=7\n","[SoftImpute] Iter 60: observed MAE=0.018056 rank=6\n","[SoftImpute] Iter 61: observed MAE=0.018056 rank=6\n","[SoftImpute] Iter 62: observed MAE=0.018055 rank=6\n","[SoftImpute] Iter 63: observed MAE=0.018055 rank=6\n","[SoftImpute] Iter 64: observed MAE=0.018054 rank=6\n","[SoftImpute] Iter 65: observed MAE=0.018054 rank=6\n","[SoftImpute] Iter 66: observed MAE=0.018054 rank=6\n","[SoftImpute] Iter 67: observed MAE=0.018054 rank=6\n","[SoftImpute] Iter 68: observed MAE=0.018053 rank=6\n","[SoftImpute] Iter 69: observed MAE=0.018053 rank=6\n","[SoftImpute] Iter 70: observed MAE=0.018053 rank=6\n","[SoftImpute] Iter 71: observed MAE=0.018053 rank=6\n","[SoftImpute] Iter 72: observed MAE=0.018053 rank=6\n","[SoftImpute] Iter 73: observed MAE=0.018053 rank=6\n","[SoftImpute] Iter 74: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 75: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 76: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 77: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 78: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 79: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 80: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 81: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 82: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 83: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 84: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 85: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 86: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 87: observed MAE=0.018052 rank=6\n","[SoftImpute] Iter 88: observed MAE=0.018051 rank=6\n","[SoftImpute] Iter 89: observed MAE=0.018051 rank=6\n","[SoftImpute] Iter 90: observed MAE=0.018051 rank=6\n","[SoftImpute] Iter 91: observed MAE=0.018051 rank=6\n","[SoftImpute] Iter 92: observed MAE=0.018051 rank=6\n","[SoftImpute] Iter 93: observed MAE=0.018051 rank=6\n","[SoftImpute] Iter 94: observed MAE=0.018051 rank=6\n","[SoftImpute] Iter 95: observed MAE=0.018051 rank=6\n","[SoftImpute] Iter 96: observed MAE=0.018050 rank=6\n","[SoftImpute] Iter 97: observed MAE=0.018050 rank=6\n","[SoftImpute] Iter 98: observed MAE=0.018050 rank=6\n","[SoftImpute] Iter 99: observed MAE=0.018050 rank=6\n","[SoftImpute] Iter 100: observed MAE=0.018050 rank=6\n","[SoftImpute] Stopped after iteration 100 for lambda=0.211166\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 21181\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 16633, constraints m = 18901\n","Cones:\tprimal zero / dual free vars: 1134\n","\tlinear vars: 3402\n","\tsd vars: 14365, sd blks: 1\n","Setup time: 1.96e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.65e+21  1.55e+21  1.00e+00 -1.44e+23  2.71e+22  3.59e+22  1.75e-02 \n","   100| 1.15e-03  1.88e-03  1.90e-04  2.06e+01  2.06e+01  1.32e-14  2.12e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.12e+00s\n","\tLin-sys: nnz in L factor: 57288, avg solve time: 4.20e-04s\n","\tCones: avg projection time: 1.50e-02s\n","\tAcceleration: avg step time: 4.55e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.4006e-09, dist(y, K*) = 1.3353e-09, s'y/|s||y| = -6.8913e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.2741e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.7016e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 6.8509e-05\n","----------------------------------------------------------------------------\n","c'x = 20.6543, -b'y = 20.6572\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.04823324, 0.08477216, 0.07722017, 0.08593229, 0.12315839,\n","       0.09009895, 0.50237026])"]},"metadata":{"tags":[]},"execution_count":20}]},{"cell_type":"code","metadata":{"id":"18T5JuhFoBGO"},"source":[""],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"Qwd77MJQKfMO"},"source":["# Parkinson dataset\n","\n","https://archive.ics.uci.edu/ml/datasets/Parkinsons\n"]},{"cell_type":"code","metadata":{"id":"VGTaZDhOKiUC","executionInfo":{"status":"ok","timestamp":1604550096971,"user_tz":360,"elapsed":870,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"42522ce2-92ea-4a72-b74d-5f1dca78382e","colab":{"base_uri":"https://localhost:8080/"}},"source":["data = pd.read_csv('http://archive.ics.uci.edu/ml/machine-learning-databases/parkinsons/parkinsons.data',\n","                  sep = \",\")\n","data = data.drop(['name'], axis = 1)\n","X, y = data.drop(['status'], axis = 1), data['status']\n","X = pd.DataFrame.to_numpy(X)\n","4/5*np.array([sum(y==0), sum(y==1)])                   "],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ 38.4, 117.6])"]},"metadata":{"tags":[]},"execution_count":21}]},{"cell_type":"markdown","metadata":{"id":"k-yzh79t9IZI"},"source":["## 20%"]},{"cell_type":"code","metadata":{"id":"fuKqlsUbGkPb","executionInfo":{"status":"ok","timestamp":1591370773331,"user_tz":300,"elapsed":38814,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"f69c71f6-35ef-449a-b580-b8dce8dd1b32","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),35,30,29],\n","                  [sum(ytrain==1),100,88, 70]])\n","    p = np.array([5,10,15,22])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,2) for k in np.arange(5)]\n","res_20 = np.mean(np.asarray(res), axis=0)\n","res_20"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 16.131710\n","[SoftImpute] Iter 1: observed MAE=0.017482 rank=16\n","[SoftImpute] Iter 2: observed MAE=0.017603 rank=16\n","[SoftImpute] Iter 3: observed MAE=0.017677 rank=16\n","[SoftImpute] Iter 4: observed MAE=0.017720 rank=16\n","[SoftImpute] Iter 5: observed MAE=0.017747 rank=16\n","[SoftImpute] Iter 6: observed MAE=0.017763 rank=16\n","[SoftImpute] Iter 7: observed MAE=0.017773 rank=16\n","[SoftImpute] Iter 8: observed MAE=0.017780 rank=16\n","[SoftImpute] Iter 9: observed MAE=0.017785 rank=16\n","[SoftImpute] Iter 10: observed MAE=0.017788 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.017791 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.017794 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.017797 rank=16\n","[SoftImpute] Iter 14: observed MAE=0.017800 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.017802 rank=16\n","[SoftImpute] Iter 16: observed MAE=0.017804 rank=16\n","[SoftImpute] Iter 17: observed MAE=0.017805 rank=16\n","[SoftImpute] Iter 18: observed MAE=0.017807 rank=16\n","[SoftImpute] Iter 19: observed MAE=0.017808 rank=16\n","[SoftImpute] Iter 20: observed MAE=0.017809 rank=16\n","[SoftImpute] Iter 21: observed MAE=0.017810 rank=16\n","[SoftImpute] Iter 22: observed MAE=0.017811 rank=16\n","[SoftImpute] Iter 23: observed MAE=0.017811 rank=16\n","[SoftImpute] Iter 24: observed MAE=0.017812 rank=16\n","[SoftImpute] Iter 25: observed MAE=0.017812 rank=16\n","[SoftImpute] Iter 26: observed MAE=0.017813 rank=16\n","[SoftImpute] Iter 27: observed MAE=0.017814 rank=16\n","[SoftImpute] Iter 28: observed 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observed MAE=0.017829 rank=16\n","[SoftImpute] Iter 47: observed MAE=0.017830 rank=16\n","[SoftImpute] Iter 48: observed MAE=0.017831 rank=16\n","[SoftImpute] Iter 49: observed MAE=0.017831 rank=16\n","[SoftImpute] Iter 50: observed MAE=0.017832 rank=16\n","[SoftImpute] Iter 51: observed MAE=0.017833 rank=16\n","[SoftImpute] Iter 52: observed MAE=0.017833 rank=16\n","[SoftImpute] Iter 53: observed MAE=0.017834 rank=16\n","[SoftImpute] Iter 54: observed MAE=0.017834 rank=16\n","[SoftImpute] Iter 55: observed MAE=0.017835 rank=16\n","[SoftImpute] Iter 56: observed MAE=0.017836 rank=16\n","[SoftImpute] Iter 57: observed MAE=0.017837 rank=16\n","[SoftImpute] Iter 58: observed MAE=0.017837 rank=16\n","[SoftImpute] Iter 59: observed MAE=0.017838 rank=16\n","[SoftImpute] Iter 60: observed MAE=0.017838 rank=16\n","[SoftImpute] Iter 61: observed MAE=0.017839 rank=16\n","[SoftImpute] Iter 62: observed MAE=0.017840 rank=16\n","[SoftImpute] Iter 63: observed MAE=0.017841 rank=16\n","[SoftImpute] Iter 64: observed MAE=0.017842 rank=16\n","[SoftImpute] Iter 65: observed MAE=0.017843 rank=16\n","[SoftImpute] Iter 66: observed MAE=0.017844 rank=16\n","[SoftImpute] Iter 67: observed MAE=0.017844 rank=16\n","[SoftImpute] Iter 68: observed MAE=0.017845 rank=16\n","[SoftImpute] Iter 69: observed MAE=0.017846 rank=16\n","[SoftImpute] Iter 70: observed MAE=0.017847 rank=16\n","[SoftImpute] Iter 71: observed MAE=0.017848 rank=16\n","[SoftImpute] Iter 72: observed MAE=0.017848 rank=16\n","[SoftImpute] Iter 73: observed MAE=0.017849 rank=16\n","[SoftImpute] Iter 74: observed MAE=0.017850 rank=16\n","[SoftImpute] Iter 75: observed MAE=0.017851 rank=16\n","[SoftImpute] Iter 76: observed MAE=0.017851 rank=16\n","[SoftImpute] Iter 77: observed MAE=0.017852 rank=16\n","[SoftImpute] Iter 78: observed MAE=0.017853 rank=16\n","[SoftImpute] Iter 79: observed MAE=0.017853 rank=16\n","[SoftImpute] Iter 80: observed MAE=0.017854 rank=16\n","[SoftImpute] Iter 81: observed MAE=0.017854 rank=16\n","[SoftImpute] Iter 82: observed MAE=0.017855 rank=16\n","[SoftImpute] Iter 83: observed MAE=0.017856 rank=15\n","[SoftImpute] Iter 84: observed MAE=0.017854 rank=15\n","[SoftImpute] Iter 85: observed MAE=0.017853 rank=15\n","[SoftImpute] Iter 86: observed MAE=0.017852 rank=15\n","[SoftImpute] Iter 87: observed MAE=0.017851 rank=15\n","[SoftImpute] Iter 88: observed MAE=0.017851 rank=15\n","[SoftImpute] Iter 89: observed MAE=0.017850 rank=15\n","[SoftImpute] Iter 90: observed MAE=0.017849 rank=15\n","[SoftImpute] Iter 91: observed MAE=0.017849 rank=15\n","[SoftImpute] Iter 92: observed MAE=0.017848 rank=15\n","[SoftImpute] Iter 93: observed MAE=0.017847 rank=15\n","[SoftImpute] Iter 94: observed MAE=0.017847 rank=15\n","[SoftImpute] Iter 95: observed MAE=0.017846 rank=15\n","[SoftImpute] Iter 96: observed MAE=0.017846 rank=15\n","[SoftImpute] Iter 97: observed MAE=0.017845 rank=15\n","[SoftImpute] Iter 98: observed MAE=0.017845 rank=15\n","[SoftImpute] Iter 99: observed MAE=0.017844 rank=15\n","[SoftImpute] Iter 100: observed MAE=0.017844 rank=15\n","[SoftImpute] Stopped after iteration 100 for lambda=0.322634\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 37087\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 21695, constraints m = 28339\n","Cones:\tprimal zero / dual free vars: 3322\n","\tlinear vars: 9966\n","\tsd vars: 15051, sd blks: 1\n","Setup time: 3.62e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.75e+21  1.68e+21  1.00e+00 -2.29e+23  4.91e+22  8.28e+22  2.23e-02 \n","   100| 1.46e-03  1.46e-03  1.24e-04  4.56e+01  4.57e+01  7.46e-15  2.39e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.39e+00s\n","\tLin-sys: nnz in L factor: 89834, avg solve time: 6.28e-04s\n","\tCones: avg projection time: 1.53e-02s\n","\tAcceleration: avg step time: 6.39e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2032e-09, dist(y, K*) = 1.9044e-08, s'y/|s||y| = -6.9747e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.1807e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 5.7248e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 7.5389e-05\n","----------------------------------------------------------------------------\n","c'x = 45.6543, -b'y = 45.6473\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 15.744300\n","[SoftImpute] Iter 1: observed MAE=0.017182 rank=16\n","[SoftImpute] Iter 2: observed MAE=0.017277 rank=16\n","[SoftImpute] Iter 3: observed MAE=0.017346 rank=16\n","[SoftImpute] Iter 4: observed MAE=0.017390 rank=16\n","[SoftImpute] Iter 5: observed MAE=0.017413 rank=16\n","[SoftImpute] Iter 6: observed MAE=0.017427 rank=16\n","[SoftImpute] Iter 7: observed MAE=0.017437 rank=16\n","[SoftImpute] Iter 8: observed MAE=0.017443 rank=16\n","[SoftImpute] Iter 9: observed MAE=0.017448 rank=16\n","[SoftImpute] Iter 10: observed MAE=0.017453 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.017460 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.017466 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.017472 rank=16\n","[SoftImpute] Iter 14: observed MAE=0.017477 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.017483 rank=16\n","[SoftImpute] Iter 16: observed MAE=0.017488 rank=16\n","[SoftImpute] Iter 17: observed MAE=0.017492 rank=16\n","[SoftImpute] Iter 18: observed MAE=0.017495 rank=16\n","[SoftImpute] Iter 19: observed MAE=0.017498 rank=16\n","[SoftImpute] Iter 20: observed MAE=0.017501 rank=16\n","[SoftImpute] Iter 21: observed MAE=0.017503 rank=16\n","[SoftImpute] Iter 22: observed MAE=0.017505 rank=16\n","[SoftImpute] Iter 23: observed MAE=0.017507 rank=16\n","[SoftImpute] Iter 24: observed MAE=0.017508 rank=16\n","[SoftImpute] Iter 25: observed MAE=0.017509 rank=16\n","[SoftImpute] Iter 26: observed MAE=0.017510 rank=16\n","[SoftImpute] Iter 27: observed MAE=0.017511 rank=16\n","[SoftImpute] Iter 28: observed 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Iter 64: observed MAE=0.017510 rank=15\n","[SoftImpute] Iter 65: observed MAE=0.017508 rank=15\n","[SoftImpute] Iter 66: observed MAE=0.017507 rank=15\n","[SoftImpute] Iter 67: observed MAE=0.017505 rank=15\n","[SoftImpute] Iter 68: observed MAE=0.017504 rank=15\n","[SoftImpute] Iter 69: observed MAE=0.017502 rank=15\n","[SoftImpute] Iter 70: observed MAE=0.017501 rank=15\n","[SoftImpute] Iter 71: observed MAE=0.017499 rank=15\n","[SoftImpute] Iter 72: observed MAE=0.017498 rank=15\n","[SoftImpute] Iter 73: observed MAE=0.017497 rank=15\n","[SoftImpute] Iter 74: observed MAE=0.017495 rank=15\n","[SoftImpute] Iter 75: observed MAE=0.017494 rank=15\n","[SoftImpute] Iter 76: observed MAE=0.017492 rank=15\n","[SoftImpute] Iter 77: observed MAE=0.017491 rank=15\n","[SoftImpute] Iter 78: observed MAE=0.017490 rank=15\n","[SoftImpute] Iter 79: observed MAE=0.017488 rank=15\n","[SoftImpute] Iter 80: observed MAE=0.017487 rank=15\n","[SoftImpute] Iter 81: observed MAE=0.017486 rank=15\n","[SoftImpute] Iter 82: observed MAE=0.017484 rank=15\n","[SoftImpute] Iter 83: observed MAE=0.017483 rank=15\n","[SoftImpute] Iter 84: observed MAE=0.017482 rank=15\n","[SoftImpute] Iter 85: observed MAE=0.017481 rank=15\n","[SoftImpute] Iter 86: observed MAE=0.017480 rank=15\n","[SoftImpute] Iter 87: observed MAE=0.017479 rank=15\n","[SoftImpute] Iter 88: observed MAE=0.017478 rank=15\n","[SoftImpute] Iter 89: observed MAE=0.017476 rank=15\n","[SoftImpute] Iter 90: observed MAE=0.017475 rank=15\n","[SoftImpute] Iter 91: observed MAE=0.017474 rank=15\n","[SoftImpute] Iter 92: observed MAE=0.017473 rank=15\n","[SoftImpute] Iter 93: observed MAE=0.017472 rank=15\n","[SoftImpute] Iter 94: observed MAE=0.017471 rank=15\n","[SoftImpute] Iter 95: observed MAE=0.017470 rank=15\n","[SoftImpute] Iter 96: observed MAE=0.017469 rank=15\n","[SoftImpute] Iter 97: observed MAE=0.017468 rank=15\n","[SoftImpute] Iter 98: observed MAE=0.017467 rank=15\n","[SoftImpute] Iter 99: observed MAE=0.017466 rank=15\n","[SoftImpute] Iter 100: observed MAE=0.017465 rank=15\n","[SoftImpute] Stopped after iteration 100 for lambda=0.314886\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 37676\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 22132, constraints m = 28864\n","Cones:\tprimal zero / dual free vars: 3366\n","\tlinear vars: 10098\n","\tsd vars: 15400, sd blks: 1\n","Setup time: 3.23e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.77e+21  1.70e+21  1.00e+00 -2.31e+23  4.95e+22  8.31e+22  2.02e-02 \n","   100| 1.48e-03  2.19e-03  7.50e-05  4.60e+01  4.60e+01  3.48e-15  2.43e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.43e+00s\n","\tLin-sys: nnz in L factor: 91395, avg solve time: 6.42e-04s\n","\tCones: avg projection time: 1.55e-02s\n","\tAcceleration: avg step time: 6.56e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.2131e-09, dist(y, K*) = 1.8949e-09, s'y/|s||y| = 1.2278e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.4270e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.1622e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.0178e-04\n","----------------------------------------------------------------------------\n","c'x = 45.9936, -b'y = 45.9749\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 16.398736\n","[SoftImpute] Iter 1: observed MAE=0.017916 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.017993 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.018039 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.018070 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.018091 rank=16\n","[SoftImpute] Iter 6: observed MAE=0.018099 rank=16\n","[SoftImpute] Iter 7: observed MAE=0.018105 rank=16\n","[SoftImpute] Iter 8: observed MAE=0.018108 rank=16\n","[SoftImpute] Iter 9: observed MAE=0.018110 rank=16\n","[SoftImpute] Iter 10: observed MAE=0.018111 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.018112 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.018114 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.018115 rank=16\n","[SoftImpute] Iter 14: observed MAE=0.018116 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.018117 rank=16\n","[SoftImpute] Iter 16: observed MAE=0.018117 rank=16\n","[SoftImpute] Iter 17: observed MAE=0.018118 rank=16\n","[SoftImpute] Iter 18: observed MAE=0.018119 rank=16\n","[SoftImpute] Iter 19: observed MAE=0.018120 rank=16\n","[SoftImpute] Iter 20: observed MAE=0.018120 rank=16\n","[SoftImpute] Iter 21: observed MAE=0.018121 rank=16\n","[SoftImpute] Iter 22: observed MAE=0.018121 rank=16\n","[SoftImpute] Iter 23: observed MAE=0.018122 rank=16\n","[SoftImpute] Iter 24: observed MAE=0.018122 rank=16\n","[SoftImpute] Iter 25: observed MAE=0.018122 rank=16\n","[SoftImpute] Iter 26: observed MAE=0.018121 rank=16\n","[SoftImpute] Iter 27: observed MAE=0.018121 rank=16\n","[SoftImpute] Iter 28: observed 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MAE=0.018063 rank=16\n","[SoftImpute] Iter 100: observed MAE=0.018063 rank=16\n","[SoftImpute] Stopped after iteration 100 for lambda=0.327975\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 40376\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 24148, constraints m = 31276\n","Cones:\tprimal zero / dual free vars: 3564\n","\tlinear vars: 10692\n","\tsd vars: 17020, sd blks: 1\n","Setup time: 3.62e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.87e+21  1.79e+21  1.00e+00 -2.57e+23  5.45e+22  9.01e+22  2.38e-02 \n","   100| 1.44e-03  1.64e-03  3.05e-05  4.70e+01  4.70e+01  6.27e-15  2.61e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.61e+00s\n","\tLin-sys: nnz in L factor: 98568, avg solve time: 6.78e-04s\n","\tCones: avg projection time: 1.65e-02s\n","\tAcceleration: avg step time: 7.16e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2341e-09, dist(y, K*) = 1.8329e-08, s'y/|s||y| = -6.0142e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.6191e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.5528e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.4813e-04\n","----------------------------------------------------------------------------\n","c'x = 47.0412, -b'y = 47.0271\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 16.374225\n","[SoftImpute] Iter 1: observed MAE=0.017745 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.017825 rank=16\n","[SoftImpute] Iter 3: observed MAE=0.017846 rank=16\n","[SoftImpute] Iter 4: observed MAE=0.017857 rank=16\n","[SoftImpute] Iter 5: observed MAE=0.017864 rank=16\n","[SoftImpute] Iter 6: observed MAE=0.017870 rank=16\n","[SoftImpute] Iter 7: observed MAE=0.017875 rank=16\n","[SoftImpute] Iter 8: observed MAE=0.017880 rank=16\n","[SoftImpute] Iter 9: observed MAE=0.017887 rank=16\n","[SoftImpute] Iter 10: observed MAE=0.017894 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.017899 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.017901 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.017896 rank=15\n","[SoftImpute] Iter 14: observed MAE=0.017880 rank=15\n","[SoftImpute] Iter 15: observed MAE=0.017870 rank=15\n","[SoftImpute] Iter 16: observed MAE=0.017862 rank=15\n","[SoftImpute] Iter 17: observed MAE=0.017856 rank=15\n","[SoftImpute] Iter 18: observed MAE=0.017852 rank=15\n","[SoftImpute] Iter 19: observed MAE=0.017849 rank=15\n","[SoftImpute] Iter 20: observed MAE=0.017847 rank=15\n","[SoftImpute] Iter 21: observed MAE=0.017845 rank=15\n","[SoftImpute] Iter 22: observed MAE=0.017844 rank=15\n","[SoftImpute] Iter 23: observed MAE=0.017842 rank=15\n","[SoftImpute] Iter 24: observed MAE=0.017841 rank=15\n","[SoftImpute] Iter 25: observed MAE=0.017840 rank=15\n","[SoftImpute] Iter 26: observed MAE=0.017838 rank=15\n","[SoftImpute] Iter 27: observed MAE=0.017837 rank=15\n","[SoftImpute] Iter 28: observed 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observed MAE=0.017822 rank=15\n","[SoftImpute] Iter 47: observed MAE=0.017821 rank=15\n","[SoftImpute] Iter 48: observed MAE=0.017820 rank=15\n","[SoftImpute] Iter 49: observed MAE=0.017820 rank=15\n","[SoftImpute] Iter 50: observed MAE=0.017819 rank=15\n","[SoftImpute] Iter 51: observed MAE=0.017818 rank=15\n","[SoftImpute] Iter 52: observed MAE=0.017818 rank=15\n","[SoftImpute] Iter 53: observed MAE=0.017817 rank=15\n","[SoftImpute] Iter 54: observed MAE=0.017816 rank=15\n","[SoftImpute] Iter 55: observed MAE=0.017816 rank=15\n","[SoftImpute] Iter 56: observed MAE=0.017815 rank=15\n","[SoftImpute] Iter 57: observed MAE=0.017815 rank=15\n","[SoftImpute] Iter 58: observed MAE=0.017814 rank=15\n","[SoftImpute] Iter 59: observed MAE=0.017814 rank=15\n","[SoftImpute] Iter 60: observed MAE=0.017813 rank=15\n","[SoftImpute] Iter 61: observed MAE=0.017813 rank=15\n","[SoftImpute] Iter 62: observed MAE=0.017813 rank=15\n","[SoftImpute] Iter 63: observed MAE=0.017812 rank=15\n","[SoftImpute] 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rank=15\n","[SoftImpute] Iter 82: observed MAE=0.017807 rank=15\n","[SoftImpute] Iter 83: observed MAE=0.017806 rank=15\n","[SoftImpute] Iter 84: observed MAE=0.017806 rank=15\n","[SoftImpute] Iter 85: observed MAE=0.017806 rank=15\n","[SoftImpute] Iter 86: observed MAE=0.017806 rank=15\n","[SoftImpute] Iter 87: observed MAE=0.017805 rank=15\n","[SoftImpute] Iter 88: observed MAE=0.017805 rank=15\n","[SoftImpute] Iter 89: observed MAE=0.017805 rank=15\n","[SoftImpute] Iter 90: observed MAE=0.017805 rank=15\n","[SoftImpute] Iter 91: observed MAE=0.017804 rank=15\n","[SoftImpute] Iter 92: observed MAE=0.017804 rank=15\n","[SoftImpute] Iter 93: observed MAE=0.017804 rank=15\n","[SoftImpute] Iter 94: observed MAE=0.017804 rank=15\n","[SoftImpute] Iter 95: observed MAE=0.017803 rank=15\n","[SoftImpute] Iter 96: observed MAE=0.017803 rank=15\n","[SoftImpute] Iter 97: observed MAE=0.017803 rank=15\n","[SoftImpute] Iter 98: observed MAE=0.017803 rank=15\n","[SoftImpute] Iter 99: observed MAE=0.017803 rank=15\n","[SoftImpute] Iter 100: observed MAE=0.017802 rank=15\n","[SoftImpute] Stopped after iteration 100 for lambda=0.327484\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 40376\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 24148, constraints m = 31276\n","Cones:\tprimal zero / dual free vars: 3564\n","\tlinear vars: 10692\n","\tsd vars: 17020, sd blks: 1\n","Setup time: 3.23e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.87e+21  1.79e+21  1.00e+00 -2.54e+23  5.40e+22  8.94e+22  2.38e-02 \n","   100| 2.22e-03  2.86e-03  1.92e-04  4.59e+01  4.59e+01  1.59e-14  2.60e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.60e+00s\n","\tLin-sys: nnz in L factor: 98568, avg solve time: 6.82e-04s\n","\tCones: avg projection time: 1.64e-02s\n","\tAcceleration: avg step time: 7.17e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3794e-09, dist(y, K*) = 7.1843e-09, s'y/|s||y| = 3.3150e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.5476e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.3659e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.6495e-04\n","----------------------------------------------------------------------------\n","c'x = 45.8886, -b'y = 45.8548\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 16.211498\n","[SoftImpute] Iter 1: observed MAE=0.017430 rank=16\n","[SoftImpute] Iter 2: observed MAE=0.017545 rank=16\n","[SoftImpute] Iter 3: observed MAE=0.017610 rank=15\n","[SoftImpute] Iter 4: observed MAE=0.017617 rank=15\n","[SoftImpute] Iter 5: observed MAE=0.017629 rank=15\n","[SoftImpute] Iter 6: observed MAE=0.017641 rank=15\n","[SoftImpute] Iter 7: observed MAE=0.017655 rank=15\n","[SoftImpute] Iter 8: observed MAE=0.017670 rank=15\n","[SoftImpute] Iter 9: observed MAE=0.017686 rank=15\n","[SoftImpute] Iter 10: observed MAE=0.017702 rank=15\n","[SoftImpute] Iter 11: observed MAE=0.017716 rank=15\n","[SoftImpute] Iter 12: observed MAE=0.017729 rank=15\n","[SoftImpute] Iter 13: observed MAE=0.017741 rank=15\n","[SoftImpute] Iter 14: observed MAE=0.017751 rank=15\n","[SoftImpute] Iter 15: observed MAE=0.017760 rank=15\n","[SoftImpute] Iter 16: observed MAE=0.017767 rank=15\n","[SoftImpute] Iter 17: observed MAE=0.017774 rank=15\n","[SoftImpute] Iter 18: observed MAE=0.017781 rank=15\n","[SoftImpute] Iter 19: observed MAE=0.017786 rank=15\n","[SoftImpute] Iter 20: observed MAE=0.017791 rank=15\n","[SoftImpute] Iter 21: observed MAE=0.017795 rank=15\n","[SoftImpute] Iter 22: observed MAE=0.017798 rank=15\n","[SoftImpute] Iter 23: observed MAE=0.017801 rank=15\n","[SoftImpute] Iter 24: observed MAE=0.017804 rank=15\n","[SoftImpute] Iter 25: observed MAE=0.017806 rank=15\n","[SoftImpute] Iter 26: observed MAE=0.017807 rank=15\n","[SoftImpute] Iter 27: observed MAE=0.017808 rank=15\n","[SoftImpute] Iter 28: observed MAE=0.017809 rank=15\n","[SoftImpute] Iter 29: observed MAE=0.017809 rank=15\n","[SoftImpute] Iter 30: observed MAE=0.017810 rank=15\n","[SoftImpute] Iter 31: observed MAE=0.017810 rank=15\n","[SoftImpute] Iter 32: observed MAE=0.017810 rank=15\n","[SoftImpute] Iter 33: observed MAE=0.017810 rank=15\n","[SoftImpute] Iter 34: observed MAE=0.017810 rank=15\n","[SoftImpute] Iter 35: observed MAE=0.017809 rank=15\n","[SoftImpute] Iter 36: observed MAE=0.017809 rank=15\n","[SoftImpute] Iter 37: observed MAE=0.017808 rank=15\n","[SoftImpute] Iter 38: observed MAE=0.017808 rank=15\n","[SoftImpute] Iter 39: observed MAE=0.017807 rank=15\n","[SoftImpute] Iter 40: observed MAE=0.017806 rank=15\n","[SoftImpute] Iter 41: observed MAE=0.017806 rank=15\n","[SoftImpute] Iter 42: observed MAE=0.017805 rank=15\n","[SoftImpute] Iter 43: observed MAE=0.017804 rank=15\n","[SoftImpute] Iter 44: observed MAE=0.017803 rank=15\n","[SoftImpute] Iter 45: observed MAE=0.017802 rank=15\n","[SoftImpute] Iter 46: observed MAE=0.017801 rank=15\n","[SoftImpute] Iter 47: observed MAE=0.017800 rank=15\n","[SoftImpute] Iter 48: observed MAE=0.017799 rank=15\n","[SoftImpute] Iter 49: observed MAE=0.017797 rank=15\n","[SoftImpute] Iter 50: observed MAE=0.017796 rank=15\n","[SoftImpute] Iter 51: observed MAE=0.017795 rank=15\n","[SoftImpute] Iter 52: observed MAE=0.017794 rank=15\n","[SoftImpute] Iter 53: observed MAE=0.017793 rank=15\n","[SoftImpute] Iter 54: observed MAE=0.017792 rank=15\n","[SoftImpute] Iter 55: observed MAE=0.017791 rank=15\n","[SoftImpute] Iter 56: observed MAE=0.017789 rank=15\n","[SoftImpute] Iter 57: observed MAE=0.017788 rank=15\n","[SoftImpute] Iter 58: observed MAE=0.017787 rank=15\n","[SoftImpute] Iter 59: observed MAE=0.017786 rank=15\n","[SoftImpute] Iter 60: observed MAE=0.017785 rank=15\n","[SoftImpute] Iter 61: observed MAE=0.017784 rank=15\n","[SoftImpute] Iter 62: observed MAE=0.017783 rank=15\n","[SoftImpute] Iter 63: observed MAE=0.017782 rank=15\n","[SoftImpute] Iter 64: observed MAE=0.017781 rank=15\n","[SoftImpute] Iter 65: observed MAE=0.017781 rank=15\n","[SoftImpute] Iter 66: observed MAE=0.017780 rank=15\n","[SoftImpute] Iter 67: observed MAE=0.017779 rank=15\n","[SoftImpute] Iter 68: observed MAE=0.017778 rank=15\n","[SoftImpute] Iter 69: observed MAE=0.017777 rank=15\n","[SoftImpute] Iter 70: observed MAE=0.017777 rank=15\n","[SoftImpute] Iter 71: observed MAE=0.017776 rank=15\n","[SoftImpute] Iter 72: observed MAE=0.017775 rank=15\n","[SoftImpute] Iter 73: observed MAE=0.017774 rank=15\n","[SoftImpute] Iter 74: observed MAE=0.017773 rank=15\n","[SoftImpute] Iter 75: observed MAE=0.017773 rank=15\n","[SoftImpute] Iter 76: observed MAE=0.017772 rank=15\n","[SoftImpute] Iter 77: observed MAE=0.017771 rank=15\n","[SoftImpute] Iter 78: observed MAE=0.017770 rank=15\n","[SoftImpute] Iter 79: observed MAE=0.017769 rank=15\n","[SoftImpute] Iter 80: observed MAE=0.017768 rank=15\n","[SoftImpute] Iter 81: observed MAE=0.017768 rank=15\n","[SoftImpute] Iter 82: observed MAE=0.017767 rank=15\n","[SoftImpute] Iter 83: observed MAE=0.017766 rank=15\n","[SoftImpute] Iter 84: observed MAE=0.017765 rank=15\n","[SoftImpute] Iter 85: observed MAE=0.017764 rank=15\n","[SoftImpute] Iter 86: observed MAE=0.017764 rank=15\n","[SoftImpute] Iter 87: observed MAE=0.017763 rank=15\n","[SoftImpute] Iter 88: observed MAE=0.017762 rank=15\n","[SoftImpute] Iter 89: observed MAE=0.017761 rank=15\n","[SoftImpute] Iter 90: observed MAE=0.017761 rank=15\n","[SoftImpute] Iter 91: observed MAE=0.017760 rank=15\n","[SoftImpute] Iter 92: observed MAE=0.017759 rank=15\n","[SoftImpute] Iter 93: observed MAE=0.017759 rank=15\n","[SoftImpute] Iter 94: observed MAE=0.017758 rank=15\n","[SoftImpute] Iter 95: observed MAE=0.017757 rank=15\n","[SoftImpute] Iter 96: observed MAE=0.017757 rank=15\n","[SoftImpute] Iter 97: observed MAE=0.017756 rank=15\n","[SoftImpute] Iter 98: observed MAE=0.017755 rank=15\n","[SoftImpute] Iter 99: observed MAE=0.017755 rank=15\n","[SoftImpute] Iter 100: observed MAE=0.017754 rank=15\n","[SoftImpute] Stopped after iteration 100 for lambda=0.324230\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 37381\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 21913, constraints m = 28601\n","Cones:\tprimal zero / dual free vars: 3344\n","\tlinear vars: 10032\n","\tsd vars: 15225, sd blks: 1\n","Setup time: 3.40e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.77e+21  1.69e+21  1.00e+00 -2.34e+23  5.01e+22  8.43e+22  3.06e-02 \n","   100| 1.93e-03  2.36e-03  3.85e-04  4.65e+01  4.64e+01  1.29e-14  2.46e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.46e+00s\n","\tLin-sys: nnz in L factor: 90613, avg solve time: 6.34e-04s\n","\tCones: avg projection time: 1.56e-02s\n","\tAcceleration: avg step time: 6.74e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1771e-09, dist(y, K*) = 8.6660e-09, s'y/|s||y| = 6.8827e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.6042e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.7130e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 8.0997e-06\n","----------------------------------------------------------------------------\n","c'x = 46.4261, -b'y = 46.4269\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.14596295, 0.15959932, 0.1824323 , 0.17788684, 0.18233162,\n","       0.18697775, 0.20164826])"]},"metadata":{"tags":[]},"execution_count":12}]},{"cell_type":"markdown","metadata":{"id":"9WlMVFJZ9Lcn"},"source":["## 30%"]},{"cell_type":"code","metadata":{"id":"tMIXsvmJYWeC","executionInfo":{"status":"ok","timestamp":1591370812235,"user_tz":300,"elapsed":75697,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"8a01da35-4903-4296-f972-d07a5d028d60","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),35,30,25],\n","                  [sum(ytrain==1),80,70, 55]])\n","    p = np.array([5,10,15,22])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,2) for k in np.arange(5)]\n","res_30 = np.mean(np.asarray(res), axis=0)\n","res_30"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 14.573724\n","[SoftImpute] Iter 1: observed MAE=0.017023 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.017181 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.017274 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.017334 rank=16\n","[SoftImpute] Iter 5: observed MAE=0.017373 rank=16\n","[SoftImpute] Iter 6: observed MAE=0.017410 rank=16\n","[SoftImpute] Iter 7: observed MAE=0.017443 rank=16\n","[SoftImpute] Iter 8: observed MAE=0.017472 rank=16\n","[SoftImpute] Iter 9: observed MAE=0.017488 rank=16\n","[SoftImpute] Iter 10: observed MAE=0.017476 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.017437 rank=15\n","[SoftImpute] Iter 12: observed MAE=0.017403 rank=15\n","[SoftImpute] Iter 13: observed MAE=0.017377 rank=15\n","[SoftImpute] Iter 14: observed MAE=0.017356 rank=15\n","[SoftImpute] Iter 15: observed MAE=0.017337 rank=15\n","[SoftImpute] Iter 16: observed MAE=0.017319 rank=15\n","[SoftImpute] Iter 17: observed MAE=0.017302 rank=14\n","[SoftImpute] Iter 18: observed MAE=0.017288 rank=14\n","[SoftImpute] Iter 19: observed MAE=0.017277 rank=14\n","[SoftImpute] Iter 20: observed MAE=0.017267 rank=14\n","[SoftImpute] Iter 21: observed MAE=0.017258 rank=14\n","[SoftImpute] Iter 22: observed MAE=0.017251 rank=14\n","[SoftImpute] Iter 23: observed MAE=0.017244 rank=14\n","[SoftImpute] Iter 24: observed MAE=0.017238 rank=14\n","[SoftImpute] Iter 25: observed MAE=0.017232 rank=14\n","[SoftImpute] Iter 26: observed MAE=0.017227 rank=14\n","[SoftImpute] Iter 27: observed MAE=0.017222 rank=14\n","[SoftImpute] Iter 28: observed MAE=0.017219 rank=14\n","[SoftImpute] Iter 29: observed MAE=0.017215 rank=14\n","[SoftImpute] Iter 30: observed MAE=0.017212 rank=14\n","[SoftImpute] Iter 31: observed MAE=0.017209 rank=14\n","[SoftImpute] Iter 32: observed MAE=0.017207 rank=14\n","[SoftImpute] Iter 33: observed MAE=0.017204 rank=14\n","[SoftImpute] Iter 34: observed MAE=0.017202 rank=14\n","[SoftImpute] Iter 35: observed MAE=0.017200 rank=14\n","[SoftImpute] Iter 36: observed MAE=0.017198 rank=14\n","[SoftImpute] Iter 37: observed 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Iter 73: observed MAE=0.017172 rank=14\n","[SoftImpute] Iter 74: observed MAE=0.017172 rank=14\n","[SoftImpute] Iter 75: observed MAE=0.017171 rank=14\n","[SoftImpute] Iter 76: observed MAE=0.017171 rank=14\n","[SoftImpute] Iter 77: observed MAE=0.017171 rank=14\n","[SoftImpute] Iter 78: observed MAE=0.017170 rank=14\n","[SoftImpute] Iter 79: observed MAE=0.017170 rank=14\n","[SoftImpute] Iter 80: observed MAE=0.017170 rank=14\n","[SoftImpute] Iter 81: observed MAE=0.017170 rank=14\n","[SoftImpute] Iter 82: observed MAE=0.017169 rank=14\n","[SoftImpute] Iter 83: observed MAE=0.017169 rank=14\n","[SoftImpute] Iter 84: observed MAE=0.017169 rank=14\n","[SoftImpute] Iter 85: observed MAE=0.017168 rank=14\n","[SoftImpute] Iter 86: observed MAE=0.017168 rank=14\n","[SoftImpute] Iter 87: observed MAE=0.017168 rank=14\n","[SoftImpute] Iter 88: observed MAE=0.017168 rank=14\n","[SoftImpute] Iter 89: observed MAE=0.017167 rank=14\n","[SoftImpute] Iter 90: observed MAE=0.017167 rank=14\n","[SoftImpute] Iter 91: observed MAE=0.017167 rank=14\n","[SoftImpute] Iter 92: observed MAE=0.017167 rank=14\n","[SoftImpute] Iter 93: observed MAE=0.017166 rank=14\n","[SoftImpute] Iter 94: observed MAE=0.017166 rank=14\n","[SoftImpute] Iter 95: observed MAE=0.017166 rank=14\n","[SoftImpute] Iter 96: observed MAE=0.017166 rank=14\n","[SoftImpute] Iter 97: observed MAE=0.017165 rank=14\n","[SoftImpute] Iter 98: observed MAE=0.017165 rank=14\n","[SoftImpute] Iter 99: observed MAE=0.017165 rank=14\n","[SoftImpute] Iter 100: observed MAE=0.017165 rank=14\n","[SoftImpute] Stopped after iteration 100 for lambda=0.291474\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 36441\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 21695, constraints m = 28339\n","Cones:\tprimal zero / dual free vars: 3322\n","\tlinear vars: 9966\n","\tsd vars: 15051, sd blks: 1\n","Setup time: 3.04e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.77e+21  1.70e+21  1.00e+00 -2.17e+23  4.64e+22  7.59e+22  1.90e-02 \n","   100| 1.39e-03  1.66e-03  2.14e-04  4.32e+01  4.32e+01  4.54e-15  2.40e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.40e+00s\n","\tLin-sys: nnz in L factor: 88865, avg solve time: 6.24e-04s\n","\tCones: avg projection time: 1.55e-02s\n","\tAcceleration: avg step time: 6.29e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.4028e-09, dist(y, K*) = 1.4761e-08, s'y/|s||y| = -3.4865e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.8552e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 8.1064e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.1805e-04\n","----------------------------------------------------------------------------\n","c'x = 43.1950, -b'y = 43.1673\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.493200\n","[SoftImpute] Iter 1: observed MAE=0.016864 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.016968 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.017027 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.017076 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.017127 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.017174 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.017179 rank=16\n","[SoftImpute] Iter 8: observed MAE=0.017138 rank=16\n","[SoftImpute] Iter 9: observed MAE=0.017111 rank=16\n","[SoftImpute] Iter 10: observed MAE=0.017091 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.017076 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.017064 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.017056 rank=16\n","[SoftImpute] Iter 14: observed MAE=0.017051 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.017048 rank=16\n","[SoftImpute] Iter 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Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 37030\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 22132, constraints m = 28864\n","Cones:\tprimal zero / dual free vars: 3366\n","\tlinear vars: 10098\n","\tsd vars: 15400, sd blks: 1\n","Setup time: 3.01e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.79e+21  1.72e+21  1.00e+00 -2.17e+23  4.65e+22  7.58e+22  2.00e-02 \n","   100| 1.16e-03  1.15e-03  1.97e-04  4.31e+01  4.31e+01  5.47e-16  2.44e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.44e+00s\n","\tLin-sys: nnz in L factor: 90426, avg solve time: 6.35e-04s\n","\tCones: avg projection time: 1.54e-02s\n","\tAcceleration: avg step time: 6.69e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.1454e-09, dist(y, K*) = 3.2601e-08, s'y/|s||y| = -6.9232e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 7.2789e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 7.1200e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.0888e-04\n","----------------------------------------------------------------------------\n","c'x = 43.0792, -b'y = 43.0610\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.827960\n","[SoftImpute] Iter 1: observed MAE=0.017130 rank=16\n","[SoftImpute] Iter 2: observed MAE=0.017196 rank=16\n","[SoftImpute] Iter 3: observed MAE=0.017265 rank=16\n","[SoftImpute] Iter 4: observed MAE=0.017313 rank=16\n","[SoftImpute] Iter 5: observed MAE=0.017326 rank=16\n","[SoftImpute] Iter 6: observed MAE=0.017314 rank=16\n","[SoftImpute] Iter 7: observed MAE=0.017296 rank=16\n","[SoftImpute] Iter 8: observed MAE=0.017276 rank=15\n","[SoftImpute] Iter 9: observed MAE=0.017258 rank=15\n","[SoftImpute] Iter 10: observed MAE=0.017248 rank=15\n","[SoftImpute] Iter 11: observed MAE=0.017244 rank=15\n","[SoftImpute] Iter 12: observed MAE=0.017242 rank=15\n","[SoftImpute] Iter 13: observed MAE=0.017241 rank=15\n","[SoftImpute] Iter 14: observed MAE=0.017242 rank=15\n","[SoftImpute] Iter 15: observed MAE=0.017243 rank=15\n","[SoftImpute] Iter 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Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 39730\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 24148, constraints m = 31276\n","Cones:\tprimal zero / dual free vars: 3564\n","\tlinear vars: 10692\n","\tsd vars: 17020, sd blks: 1\n","Setup time: 3.45e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.88e+21  1.81e+21  1.00e+00 -2.45e+23  5.19e+22  8.36e+22  2.16e-02 \n","   100| 1.18e-03  1.08e-03  1.49e-04  4.52e+01  4.52e+01  1.88e-15  2.60e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.60e+00s\n","\tLin-sys: nnz in L factor: 97599, avg solve time: 6.87e-04s\n","\tCones: avg projection time: 1.64e-02s\n","\tAcceleration: avg step time: 7.08e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2577e-09, dist(y, K*) = 1.2833e-08, s'y/|s||y| = -6.8630e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.0252e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.8167e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.0837e-04\n","----------------------------------------------------------------------------\n","c'x = 45.2208, -b'y = 45.2018\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.598650\n","[SoftImpute] Iter 1: observed MAE=0.016792 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.016941 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.016992 rank=16\n","[SoftImpute] Iter 4: observed MAE=0.017050 rank=16\n","[SoftImpute] Iter 5: observed MAE=0.017093 rank=16\n","[SoftImpute] Iter 6: observed MAE=0.017093 rank=15\n","[SoftImpute] Iter 7: observed MAE=0.017034 rank=15\n","[SoftImpute] Iter 8: observed MAE=0.016997 rank=15\n","[SoftImpute] Iter 9: observed MAE=0.016971 rank=15\n","[SoftImpute] Iter 10: observed MAE=0.016952 rank=15\n","[SoftImpute] Iter 11: observed MAE=0.016938 rank=15\n","[SoftImpute] Iter 12: observed MAE=0.016928 rank=15\n","[SoftImpute] Iter 13: observed MAE=0.016921 rank=15\n","[SoftImpute] Iter 14: observed MAE=0.016917 rank=15\n","[SoftImpute] Iter 15: observed MAE=0.016914 rank=15\n","[SoftImpute] Iter 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rank=15\n","[SoftImpute] Iter 34: observed MAE=0.016916 rank=15\n","[SoftImpute] Iter 35: observed MAE=0.016917 rank=15\n","[SoftImpute] Iter 36: observed MAE=0.016918 rank=15\n","[SoftImpute] Iter 37: observed MAE=0.016918 rank=15\n","[SoftImpute] Iter 38: observed MAE=0.016918 rank=15\n","[SoftImpute] Iter 39: observed MAE=0.016919 rank=15\n","[SoftImpute] Iter 40: observed MAE=0.016919 rank=15\n","[SoftImpute] Iter 41: observed MAE=0.016920 rank=15\n","[SoftImpute] Iter 42: observed MAE=0.016921 rank=15\n","[SoftImpute] Iter 43: observed MAE=0.016921 rank=15\n","[SoftImpute] Iter 44: observed MAE=0.016922 rank=15\n","[SoftImpute] Iter 45: observed MAE=0.016922 rank=15\n","[SoftImpute] Iter 46: observed MAE=0.016923 rank=15\n","[SoftImpute] Iter 47: observed MAE=0.016923 rank=15\n","[SoftImpute] Iter 48: observed MAE=0.016924 rank=15\n","[SoftImpute] Iter 49: observed MAE=0.016924 rank=15\n","[SoftImpute] Iter 50: observed MAE=0.016924 rank=15\n","[SoftImpute] Iter 51: observed 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observed MAE=0.016931 rank=15\n","[SoftImpute] Iter 70: observed MAE=0.016931 rank=15\n","[SoftImpute] Iter 71: observed MAE=0.016932 rank=15\n","[SoftImpute] Iter 72: observed MAE=0.016932 rank=15\n","[SoftImpute] Iter 73: observed MAE=0.016932 rank=15\n","[SoftImpute] Iter 74: observed MAE=0.016932 rank=15\n","[SoftImpute] Iter 75: observed MAE=0.016932 rank=15\n","[SoftImpute] Iter 76: observed MAE=0.016932 rank=15\n","[SoftImpute] Iter 77: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 78: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 79: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 80: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 81: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 82: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 83: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 84: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 85: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 86: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 87: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 88: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 89: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 90: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 91: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 92: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 93: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 94: observed MAE=0.016933 rank=15\n","[SoftImpute] Iter 95: observed MAE=0.016934 rank=15\n","[SoftImpute] Iter 96: observed MAE=0.016934 rank=15\n","[SoftImpute] Iter 97: observed MAE=0.016934 rank=15\n","[SoftImpute] Iter 98: observed MAE=0.016934 rank=15\n","[SoftImpute] Iter 99: observed MAE=0.016934 rank=15\n","[SoftImpute] Iter 100: observed MAE=0.016934 rank=15\n","[SoftImpute] Stopped after iteration 100 for lambda=0.291973\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 39730\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 24148, constraints m = 31276\n","Cones:\tprimal zero / dual free vars: 3564\n","\tlinear vars: 10692\n","\tsd vars: 17020, sd blks: 1\n","Setup time: 3.13e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.88e+21  1.81e+21  1.00e+00 -2.41e+23  5.12e+22  8.25e+22  2.10e-02 \n","   100| 1.92e-03  2.83e-03  1.41e-04  4.44e+01  4.44e+01  9.71e-16  2.60e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.60e+00s\n","\tLin-sys: nnz in L factor: 97599, avg solve time: 6.78e-04s\n","\tCones: avg projection time: 1.65e-02s\n","\tAcceleration: avg step time: 7.08e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3422e-09, dist(y, K*) = 1.9512e-09, s'y/|s||y| = -9.7327e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.7333e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 7.3467e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.1549e-04\n","----------------------------------------------------------------------------\n","c'x = 44.4054, -b'y = 44.4337\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.429550\n","[SoftImpute] Iter 1: observed MAE=0.016723 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.016838 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.016899 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.016942 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.016986 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.017022 rank=16\n","[SoftImpute] Iter 7: observed MAE=0.017002 rank=16\n","[SoftImpute] Iter 8: observed MAE=0.016968 rank=16\n","[SoftImpute] Iter 9: observed MAE=0.016938 rank=16\n","[SoftImpute] Iter 10: observed MAE=0.016911 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.016892 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.016878 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.016868 rank=16\n","[SoftImpute] Iter 14: observed MAE=0.016861 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.016855 rank=16\n","[SoftImpute] Iter 16: observed MAE=0.016852 rank=16\n","[SoftImpute] Iter 17: observed MAE=0.016849 rank=16\n","[SoftImpute] Iter 18: observed MAE=0.016847 rank=16\n","[SoftImpute] Iter 19: observed MAE=0.016846 rank=16\n","[SoftImpute] Iter 20: observed MAE=0.016845 rank=16\n","[SoftImpute] Iter 21: observed MAE=0.016844 rank=16\n","[SoftImpute] Iter 22: observed MAE=0.016843 rank=16\n","[SoftImpute] Iter 23: observed MAE=0.016843 rank=16\n","[SoftImpute] Iter 24: observed MAE=0.016842 rank=16\n","[SoftImpute] Iter 25: observed MAE=0.016842 rank=16\n","[SoftImpute] Iter 26: observed MAE=0.016841 rank=16\n","[SoftImpute] Iter 27: observed MAE=0.016841 rank=16\n","[SoftImpute] Iter 28: observed MAE=0.016841 rank=16\n","[SoftImpute] Iter 29: observed MAE=0.016841 rank=16\n","[SoftImpute] Iter 30: observed MAE=0.016841 rank=16\n","[SoftImpute] Iter 31: observed MAE=0.016841 rank=16\n","[SoftImpute] Iter 32: observed MAE=0.016841 rank=16\n","[SoftImpute] Iter 33: observed MAE=0.016840 rank=16\n","[SoftImpute] Iter 34: observed MAE=0.016840 rank=16\n","[SoftImpute] Iter 35: observed MAE=0.016840 rank=16\n","[SoftImpute] Iter 36: observed MAE=0.016839 rank=16\n","[SoftImpute] Iter 37: observed MAE=0.016839 rank=16\n","[SoftImpute] Iter 38: observed MAE=0.016839 rank=16\n","[SoftImpute] Iter 39: observed MAE=0.016838 rank=16\n","[SoftImpute] Iter 40: observed MAE=0.016838 rank=16\n","[SoftImpute] Iter 41: observed MAE=0.016838 rank=16\n","[SoftImpute] Iter 42: observed MAE=0.016837 rank=16\n","[SoftImpute] Iter 43: observed MAE=0.016837 rank=16\n","[SoftImpute] Iter 44: observed MAE=0.016836 rank=16\n","[SoftImpute] Iter 45: observed MAE=0.016836 rank=16\n","[SoftImpute] Iter 46: observed MAE=0.016835 rank=16\n","[SoftImpute] Iter 47: observed MAE=0.016835 rank=16\n","[SoftImpute] Iter 48: observed MAE=0.016834 rank=16\n","[SoftImpute] Iter 49: observed MAE=0.016834 rank=16\n","[SoftImpute] Iter 50: observed MAE=0.016833 rank=16\n","[SoftImpute] Iter 51: observed 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observed MAE=0.016824 rank=16\n","[SoftImpute] Iter 70: observed MAE=0.016823 rank=16\n","[SoftImpute] Iter 71: observed MAE=0.016823 rank=16\n","[SoftImpute] Iter 72: observed MAE=0.016822 rank=16\n","[SoftImpute] Iter 73: observed MAE=0.016822 rank=16\n","[SoftImpute] Iter 74: observed MAE=0.016822 rank=16\n","[SoftImpute] Iter 75: observed MAE=0.016821 rank=16\n","[SoftImpute] Iter 76: observed MAE=0.016821 rank=16\n","[SoftImpute] Iter 77: observed MAE=0.016820 rank=16\n","[SoftImpute] Iter 78: observed MAE=0.016820 rank=16\n","[SoftImpute] Iter 79: observed MAE=0.016820 rank=16\n","[SoftImpute] Iter 80: observed MAE=0.016819 rank=16\n","[SoftImpute] Iter 81: observed MAE=0.016819 rank=16\n","[SoftImpute] Iter 82: observed MAE=0.016818 rank=16\n","[SoftImpute] Iter 83: observed MAE=0.016818 rank=16\n","[SoftImpute] Iter 84: observed MAE=0.016818 rank=16\n","[SoftImpute] Iter 85: observed MAE=0.016817 rank=16\n","[SoftImpute] Iter 86: observed MAE=0.016817 rank=16\n","[SoftImpute] Iter 87: observed MAE=0.016817 rank=16\n","[SoftImpute] Iter 88: observed MAE=0.016817 rank=16\n","[SoftImpute] Iter 89: observed MAE=0.016816 rank=16\n","[SoftImpute] Iter 90: observed MAE=0.016816 rank=16\n","[SoftImpute] Iter 91: observed MAE=0.016816 rank=16\n","[SoftImpute] Iter 92: observed MAE=0.016816 rank=16\n","[SoftImpute] Iter 93: observed MAE=0.016815 rank=16\n","[SoftImpute] Iter 94: observed MAE=0.016815 rank=16\n","[SoftImpute] Iter 95: observed MAE=0.016815 rank=16\n","[SoftImpute] Iter 96: observed MAE=0.016815 rank=16\n","[SoftImpute] Iter 97: observed MAE=0.016814 rank=16\n","[SoftImpute] Iter 98: observed MAE=0.016814 rank=16\n","[SoftImpute] Iter 99: observed MAE=0.016814 rank=16\n","[SoftImpute] Iter 100: observed MAE=0.016814 rank=16\n","[SoftImpute] Stopped after iteration 100 for lambda=0.288591\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 36735\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 21913, constraints m = 28601\n","Cones:\tprimal zero / dual free vars: 3344\n","\tlinear vars: 10032\n","\tsd vars: 15225, sd blks: 1\n","Setup time: 3.31e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.78e+21  1.71e+21  1.00e+00 -2.17e+23  4.65e+22  7.60e+22  2.13e-02 \n","   100| 8.57e-04  1.53e-03  1.50e-04  4.36e+01  4.36e+01  2.39e-14  2.39e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.39e+00s\n","\tLin-sys: nnz in L factor: 89644, avg solve time: 6.36e-04s\n","\tCones: avg projection time: 1.53e-02s\n","\tAcceleration: avg step time: 6.38e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2669e-09, dist(y, K*) = 4.4024e-09, s'y/|s||y| = 6.0243e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.0663e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.7145e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.8221e-05\n","----------------------------------------------------------------------------\n","c'x = 43.5574, -b'y = 43.5550\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.15214437, 0.18730494, 0.19012383, 0.18233666, 0.16837813,\n","       0.20116279, 0.29585588])"]},"metadata":{"tags":[]},"execution_count":13}]},{"cell_type":"markdown","metadata":{"id":"hFkG9R7k9Qof"},"source":["## 40%"]},{"cell_type":"code","metadata":{"id":"KBLbdSr4BrD5","executionInfo":{"status":"ok","timestamp":1591370853064,"user_tz":300,"elapsed":115109,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"22789b20-89a0-40c2-e893-b8520608a9ba","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),30,25,21],\n","                  [sum(ytrain==1),59,50,45]])\n","    p = np.array([5,10,15,22])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,2) for k in np.arange(5)]\n","res_40 = np.mean(np.asarray(res), axis=0)\n","res_40"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 14.023882\n","[SoftImpute] Iter 1: observed MAE=0.017928 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.017928 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.017939 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.017949 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.017959 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.017970 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.017976 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.017979 rank=17\n","[SoftImpute] Iter 9: observed MAE=0.017982 rank=17\n","[SoftImpute] Iter 10: observed MAE=0.017985 rank=17\n","[SoftImpute] Iter 11: observed MAE=0.017988 rank=17\n","[SoftImpute] Iter 12: observed MAE=0.017991 rank=17\n","[SoftImpute] Iter 13: observed MAE=0.017993 rank=17\n","[SoftImpute] Iter 14: observed MAE=0.017995 rank=17\n","[SoftImpute] Iter 15: observed MAE=0.017996 rank=17\n","[SoftImpute] Iter 16: observed MAE=0.017997 rank=17\n","[SoftImpute] Iter 17: observed MAE=0.017999 rank=17\n","[SoftImpute] Iter 18: observed MAE=0.018000 rank=17\n","[SoftImpute] Iter 19: observed MAE=0.018000 rank=17\n","[SoftImpute] Iter 20: observed MAE=0.018001 rank=17\n","[SoftImpute] Iter 21: observed MAE=0.018001 rank=17\n","[SoftImpute] Iter 22: observed MAE=0.018001 rank=17\n","[SoftImpute] Iter 23: observed MAE=0.018001 rank=17\n","[SoftImpute] Iter 24: observed MAE=0.018001 rank=17\n","[SoftImpute] Iter 25: observed MAE=0.018001 rank=17\n","[SoftImpute] Iter 26: observed MAE=0.018000 rank=17\n","[SoftImpute] Iter 27: observed 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MAE=0.017957 rank=17\n","[SoftImpute] Iter 99: observed MAE=0.017957 rank=17\n","[SoftImpute] Iter 100: observed MAE=0.017957 rank=17\n","[SoftImpute] Stopped after iteration 100 for lambda=0.280478\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 35735\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 21695, constraints m = 28339\n","Cones:\tprimal zero / dual free vars: 3322\n","\tlinear vars: 9966\n","\tsd vars: 15051, sd blks: 1\n","Setup time: 3.11e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.79e+21  1.72e+21  1.00e+00 -2.13e+23  4.57e+22  7.23e+22  2.20e-02 \n","   100| 2.12e-03  3.02e-03  1.37e-04  4.46e+01  4.46e+01  7.79e-15  2.42e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.42e+00s\n","\tLin-sys: nnz in L factor: 87806, avg solve time: 6.38e-04s\n","\tCones: avg projection time: 1.54e-02s\n","\tAcceleration: avg step time: 6.59e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1488e-09, dist(y, K*) = 6.6637e-09, s'y/|s||y| = 4.2480e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.9741e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.3051e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.6070e-04\n","----------------------------------------------------------------------------\n","c'x = 44.6274, -b'y = 44.6129\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.569719\n","[SoftImpute] Iter 1: observed MAE=0.016815 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.016845 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.016875 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.016903 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.016930 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.016955 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.016981 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.017004 rank=17\n","[SoftImpute] Iter 9: observed MAE=0.017026 rank=17\n","[SoftImpute] Iter 10: observed MAE=0.017046 rank=17\n","[SoftImpute] Iter 11: observed MAE=0.017063 rank=17\n","[SoftImpute] Iter 12: observed MAE=0.017079 rank=17\n","[SoftImpute] Iter 13: observed MAE=0.017092 rank=17\n","[SoftImpute] Iter 14: observed MAE=0.017104 rank=17\n","[SoftImpute] Iter 15: observed MAE=0.017114 rank=17\n","[SoftImpute] Iter 16: observed MAE=0.017123 rank=17\n","[SoftImpute] Iter 17: observed MAE=0.017131 rank=17\n","[SoftImpute] Iter 18: observed MAE=0.017139 rank=17\n","[SoftImpute] Iter 19: observed MAE=0.017145 rank=17\n","[SoftImpute] Iter 20: observed MAE=0.017151 rank=17\n","[SoftImpute] Iter 21: observed MAE=0.017156 rank=17\n","[SoftImpute] Iter 22: observed MAE=0.017160 rank=17\n","[SoftImpute] Iter 23: observed MAE=0.017164 rank=17\n","[SoftImpute] Iter 24: observed MAE=0.017169 rank=17\n","[SoftImpute] Iter 25: observed MAE=0.017173 rank=17\n","[SoftImpute] Iter 26: observed MAE=0.017176 rank=17\n","[SoftImpute] Iter 27: observed 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MAE=0.017217 rank=17\n","[SoftImpute] Iter 99: observed MAE=0.017217 rank=17\n","[SoftImpute] Iter 100: observed MAE=0.017217 rank=17\n","[SoftImpute] Stopped after iteration 100 for lambda=0.271394\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 36324\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 22132, constraints m = 28864\n","Cones:\tprimal zero / dual free vars: 3366\n","\tlinear vars: 10098\n","\tsd vars: 15400, sd blks: 1\n","Setup time: 3.34e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.81e+21  1.74e+21  1.00e+00 -2.13e+23  4.56e+22  7.20e+22  2.06e-02 \n","   100| 2.32e-03  3.37e-03  1.93e-05  4.37e+01  4.37e+01  2.88e-15  2.41e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.41e+00s\n","\tLin-sys: nnz in L factor: 89367, avg solve time: 6.24e-04s\n","\tCones: avg projection time: 1.52e-02s\n","\tAcceleration: avg step time: 6.62e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.5932e-09, dist(y, K*) = 2.3594e-09, s'y/|s||y| = 4.0577e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.7169e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 7.2065e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.1699e-04\n","----------------------------------------------------------------------------\n","c'x = 43.7290, -b'y = 43.7098\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.269920\n","[SoftImpute] Iter 1: observed MAE=0.018040 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.018074 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.018099 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.018113 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.018120 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.018124 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.018126 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.018128 rank=17\n","[SoftImpute] Iter 9: observed MAE=0.018128 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rank=17\n","[SoftImpute] Iter 81: observed MAE=0.018068 rank=17\n","[SoftImpute] Iter 82: observed MAE=0.018067 rank=17\n","[SoftImpute] Iter 83: observed MAE=0.018066 rank=17\n","[SoftImpute] Iter 84: observed MAE=0.018066 rank=17\n","[SoftImpute] Iter 85: observed MAE=0.018065 rank=17\n","[SoftImpute] Iter 86: observed MAE=0.018065 rank=17\n","[SoftImpute] Iter 87: observed MAE=0.018064 rank=17\n","[SoftImpute] Iter 88: observed MAE=0.018064 rank=17\n","[SoftImpute] Iter 89: observed MAE=0.018063 rank=17\n","[SoftImpute] Iter 90: observed MAE=0.018063 rank=17\n","[SoftImpute] Iter 91: observed MAE=0.018062 rank=17\n","[SoftImpute] Iter 92: observed MAE=0.018062 rank=17\n","[SoftImpute] Iter 93: observed MAE=0.018061 rank=17\n","[SoftImpute] Iter 94: observed MAE=0.018061 rank=17\n","[SoftImpute] Iter 95: observed MAE=0.018060 rank=17\n","[SoftImpute] Iter 96: observed MAE=0.018060 rank=17\n","[SoftImpute] Iter 97: observed MAE=0.018059 rank=17\n","[SoftImpute] Iter 98: observed MAE=0.018059 rank=17\n","[SoftImpute] Iter 99: observed MAE=0.018059 rank=17\n","[SoftImpute] Iter 100: observed MAE=0.018058 rank=17\n","[SoftImpute] Stopped after iteration 100 for lambda=0.285398\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 39024\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 24148, constraints m = 31276\n","Cones:\tprimal zero / dual free vars: 3564\n","\tlinear vars: 10692\n","\tsd vars: 17020, sd blks: 1\n","Setup time: 3.22e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.90e+21  1.83e+21  1.00e+00 -2.40e+23  5.09e+22  7.95e+22  2.22e-02 \n","   100| 1.97e-03  2.50e-03  5.38e-04  4.56e+01  4.56e+01  1.37e-14  2.54e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.55e+00s\n","\tLin-sys: nnz in L factor: 96540, avg solve time: 6.70e-04s\n","\tCones: avg projection time: 1.60e-02s\n","\tAcceleration: avg step time: 7.03e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3454e-09, dist(y, K*) = 2.1166e-08, s'y/|s||y| = -2.0578e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.7472e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 7.0939e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.8325e-04\n","----------------------------------------------------------------------------\n","c'x = 45.6576, -b'y = 45.6222\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.443391\n","[SoftImpute] Iter 1: observed MAE=0.018309 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.018304 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.018314 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.018319 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.018319 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.018318 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.018316 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.018314 rank=17\n","[SoftImpute] Iter 9: observed MAE=0.018312 rank=17\n","[SoftImpute] Iter 10: observed MAE=0.018311 rank=17\n","[SoftImpute] Iter 11: observed MAE=0.018311 rank=17\n","[SoftImpute] Iter 12: observed MAE=0.018312 rank=17\n","[SoftImpute] Iter 13: observed MAE=0.018312 rank=17\n","[SoftImpute] Iter 14: observed MAE=0.018313 rank=17\n","[SoftImpute] Iter 15: observed MAE=0.018314 rank=17\n","[SoftImpute] Iter 16: observed MAE=0.018315 rank=17\n","[SoftImpute] Iter 17: observed MAE=0.018315 rank=17\n","[SoftImpute] Iter 18: observed MAE=0.018315 rank=17\n","[SoftImpute] Iter 19: observed MAE=0.018316 rank=17\n","[SoftImpute] Iter 20: observed MAE=0.018317 rank=17\n","[SoftImpute] Iter 21: observed MAE=0.018318 rank=17\n","[SoftImpute] Iter 22: observed MAE=0.018319 rank=17\n","[SoftImpute] Iter 23: observed MAE=0.018319 rank=17\n","[SoftImpute] Iter 24: observed MAE=0.018319 rank=17\n","[SoftImpute] Iter 25: observed MAE=0.018318 rank=17\n","[SoftImpute] Iter 26: observed MAE=0.018318 rank=17\n","[SoftImpute] Iter 27: observed 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observed MAE=0.018301 rank=17\n","[SoftImpute] Iter 46: observed MAE=0.018300 rank=17\n","[SoftImpute] Iter 47: observed MAE=0.018299 rank=17\n","[SoftImpute] Iter 48: observed MAE=0.018298 rank=17\n","[SoftImpute] Iter 49: observed MAE=0.018297 rank=17\n","[SoftImpute] Iter 50: observed MAE=0.018296 rank=17\n","[SoftImpute] Iter 51: observed MAE=0.018295 rank=17\n","[SoftImpute] Iter 52: observed MAE=0.018294 rank=17\n","[SoftImpute] Iter 53: observed MAE=0.018294 rank=17\n","[SoftImpute] Iter 54: observed MAE=0.018293 rank=17\n","[SoftImpute] Iter 55: observed MAE=0.018291 rank=17\n","[SoftImpute] Iter 56: observed MAE=0.018290 rank=17\n","[SoftImpute] Iter 57: observed MAE=0.018289 rank=17\n","[SoftImpute] Iter 58: observed MAE=0.018288 rank=17\n","[SoftImpute] Iter 59: observed MAE=0.018287 rank=17\n","[SoftImpute] Iter 60: observed MAE=0.018286 rank=17\n","[SoftImpute] Iter 61: observed MAE=0.018285 rank=17\n","[SoftImpute] Iter 62: observed MAE=0.018284 rank=17\n","[SoftImpute] Iter 63: observed MAE=0.018283 rank=17\n","[SoftImpute] Iter 64: observed MAE=0.018282 rank=17\n","[SoftImpute] Iter 65: observed MAE=0.018282 rank=17\n","[SoftImpute] Iter 66: observed MAE=0.018281 rank=17\n","[SoftImpute] Iter 67: observed MAE=0.018280 rank=17\n","[SoftImpute] Iter 68: observed MAE=0.018279 rank=17\n","[SoftImpute] Iter 69: observed MAE=0.018278 rank=17\n","[SoftImpute] Iter 70: observed MAE=0.018277 rank=17\n","[SoftImpute] Iter 71: observed MAE=0.018277 rank=17\n","[SoftImpute] Iter 72: observed MAE=0.018276 rank=17\n","[SoftImpute] Iter 73: observed MAE=0.018275 rank=17\n","[SoftImpute] Iter 74: observed MAE=0.018274 rank=17\n","[SoftImpute] Iter 75: observed MAE=0.018274 rank=17\n","[SoftImpute] Iter 76: observed MAE=0.018273 rank=17\n","[SoftImpute] Iter 77: observed MAE=0.018272 rank=17\n","[SoftImpute] Iter 78: observed MAE=0.018271 rank=17\n","[SoftImpute] Iter 79: observed MAE=0.018271 rank=17\n","[SoftImpute] Iter 80: observed MAE=0.018270 rank=17\n","[SoftImpute] Iter 81: observed MAE=0.018269 rank=17\n","[SoftImpute] Iter 82: observed MAE=0.018269 rank=17\n","[SoftImpute] Iter 83: observed MAE=0.018268 rank=17\n","[SoftImpute] Iter 84: observed MAE=0.018268 rank=17\n","[SoftImpute] Iter 85: observed MAE=0.018267 rank=17\n","[SoftImpute] Iter 86: observed MAE=0.018266 rank=17\n","[SoftImpute] Iter 87: observed MAE=0.018266 rank=17\n","[SoftImpute] Iter 88: observed MAE=0.018265 rank=17\n","[SoftImpute] Iter 89: observed MAE=0.018265 rank=17\n","[SoftImpute] Iter 90: observed MAE=0.018264 rank=17\n","[SoftImpute] Iter 91: observed MAE=0.018264 rank=17\n","[SoftImpute] Iter 92: observed MAE=0.018263 rank=17\n","[SoftImpute] Iter 93: observed MAE=0.018263 rank=17\n","[SoftImpute] Iter 94: observed MAE=0.018262 rank=17\n","[SoftImpute] Iter 95: observed MAE=0.018262 rank=17\n","[SoftImpute] Iter 96: observed MAE=0.018262 rank=17\n","[SoftImpute] Iter 97: observed MAE=0.018261 rank=17\n","[SoftImpute] Iter 98: observed MAE=0.018261 rank=17\n","[SoftImpute] Iter 99: observed MAE=0.018261 rank=17\n","[SoftImpute] Iter 100: observed MAE=0.018260 rank=17\n","[SoftImpute] Stopped after iteration 100 for lambda=0.288868\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 39024\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 24148, constraints m = 31276\n","Cones:\tprimal zero / dual free vars: 3564\n","\tlinear vars: 10692\n","\tsd vars: 17020, sd blks: 1\n","Setup time: 3.34e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.90e+21  1.83e+21  1.00e+00 -2.40e+23  5.10e+22  7.95e+22  2.05e-02 \n","   100| 7.16e-04  9.62e-04  7.44e-05  4.57e+01  4.57e+01  6.43e-15  2.54e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.54e+00s\n","\tLin-sys: nnz in L factor: 96540, avg solve time: 6.76e-04s\n","\tCones: avg projection time: 1.61e-02s\n","\tAcceleration: avg step time: 6.89e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2392e-09, dist(y, K*) = 1.6828e-09, s'y/|s||y| = 3.0318e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.6372e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 7.3461e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.5933e-04\n","----------------------------------------------------------------------------\n","c'x = 45.7702, -b'y = 45.7554\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.638175\n","[SoftImpute] Iter 1: observed MAE=0.016821 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.016831 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.016845 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.016860 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.016875 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.016891 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.016905 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.016918 rank=17\n","[SoftImpute] Iter 9: observed MAE=0.016930 rank=17\n","[SoftImpute] Iter 10: observed MAE=0.016941 rank=17\n","[SoftImpute] Iter 11: observed MAE=0.016952 rank=17\n","[SoftImpute] Iter 12: observed MAE=0.016962 rank=17\n","[SoftImpute] Iter 13: observed MAE=0.016972 rank=17\n","[SoftImpute] Iter 14: observed MAE=0.016980 rank=17\n","[SoftImpute] Iter 15: observed MAE=0.016986 rank=17\n","[SoftImpute] Iter 16: observed MAE=0.016992 rank=17\n","[SoftImpute] Iter 17: observed MAE=0.016997 rank=17\n","[SoftImpute] Iter 18: observed MAE=0.017001 rank=17\n","[SoftImpute] Iter 19: observed MAE=0.017004 rank=17\n","[SoftImpute] Iter 20: observed MAE=0.017007 rank=17\n","[SoftImpute] Iter 21: observed MAE=0.017008 rank=17\n","[SoftImpute] Iter 22: observed MAE=0.017010 rank=17\n","[SoftImpute] Iter 23: observed MAE=0.017011 rank=17\n","[SoftImpute] Iter 24: observed MAE=0.017012 rank=17\n","[SoftImpute] Iter 25: observed MAE=0.017012 rank=17\n","[SoftImpute] Iter 26: observed MAE=0.017013 rank=17\n","[SoftImpute] Iter 27: observed MAE=0.017013 rank=17\n","[SoftImpute] Iter 28: observed MAE=0.017013 rank=17\n","[SoftImpute] Iter 29: observed MAE=0.017013 rank=17\n","[SoftImpute] Iter 30: observed MAE=0.017012 rank=17\n","[SoftImpute] Iter 31: observed MAE=0.017012 rank=17\n","[SoftImpute] Iter 32: observed MAE=0.017011 rank=17\n","[SoftImpute] Iter 33: observed MAE=0.017011 rank=17\n","[SoftImpute] Iter 34: observed MAE=0.017010 rank=17\n","[SoftImpute] Iter 35: observed MAE=0.017009 rank=17\n","[SoftImpute] Iter 36: observed MAE=0.017009 rank=17\n","[SoftImpute] Iter 37: observed MAE=0.017008 rank=17\n","[SoftImpute] Iter 38: observed MAE=0.017007 rank=17\n","[SoftImpute] Iter 39: observed MAE=0.017006 rank=17\n","[SoftImpute] Iter 40: observed MAE=0.017006 rank=17\n","[SoftImpute] Iter 41: observed MAE=0.017005 rank=17\n","[SoftImpute] Iter 42: observed MAE=0.017004 rank=17\n","[SoftImpute] Iter 43: observed MAE=0.017004 rank=17\n","[SoftImpute] Iter 44: observed MAE=0.017003 rank=17\n","[SoftImpute] Iter 45: observed MAE=0.017002 rank=17\n","[SoftImpute] Iter 46: observed MAE=0.017002 rank=17\n","[SoftImpute] Iter 47: observed MAE=0.017001 rank=17\n","[SoftImpute] Iter 48: observed MAE=0.017001 rank=17\n","[SoftImpute] Iter 49: observed MAE=0.017000 rank=17\n","[SoftImpute] Iter 50: observed MAE=0.017000 rank=17\n","[SoftImpute] Iter 51: observed MAE=0.016999 rank=17\n","[SoftImpute] Iter 52: observed MAE=0.016998 rank=17\n","[SoftImpute] Iter 53: observed MAE=0.016998 rank=17\n","[SoftImpute] Iter 54: observed MAE=0.016997 rank=17\n","[SoftImpute] Iter 55: observed MAE=0.016997 rank=17\n","[SoftImpute] Iter 56: observed MAE=0.016996 rank=17\n","[SoftImpute] Iter 57: observed MAE=0.016995 rank=17\n","[SoftImpute] Iter 58: observed MAE=0.016995 rank=17\n","[SoftImpute] Iter 59: observed MAE=0.016994 rank=17\n","[SoftImpute] Iter 60: observed MAE=0.016993 rank=17\n","[SoftImpute] Iter 61: observed MAE=0.016993 rank=17\n","[SoftImpute] Iter 62: observed MAE=0.016992 rank=17\n","[SoftImpute] Iter 63: observed MAE=0.016991 rank=17\n","[SoftImpute] Iter 64: observed MAE=0.016991 rank=17\n","[SoftImpute] Iter 65: observed MAE=0.016990 rank=17\n","[SoftImpute] Iter 66: observed MAE=0.016990 rank=17\n","[SoftImpute] Iter 67: observed MAE=0.016990 rank=17\n","[SoftImpute] Iter 68: observed MAE=0.016989 rank=17\n","[SoftImpute] Iter 69: observed MAE=0.016989 rank=17\n","[SoftImpute] Iter 70: observed MAE=0.016988 rank=17\n","[SoftImpute] Iter 71: observed MAE=0.016988 rank=17\n","[SoftImpute] Iter 72: observed MAE=0.016987 rank=17\n","[SoftImpute] Iter 73: observed MAE=0.016987 rank=17\n","[SoftImpute] Iter 74: observed MAE=0.016987 rank=17\n","[SoftImpute] Iter 75: observed MAE=0.016986 rank=17\n","[SoftImpute] Iter 76: observed MAE=0.016986 rank=17\n","[SoftImpute] Iter 77: observed MAE=0.016986 rank=17\n","[SoftImpute] Iter 78: observed MAE=0.016985 rank=17\n","[SoftImpute] Iter 79: observed MAE=0.016985 rank=17\n","[SoftImpute] Iter 80: observed MAE=0.016984 rank=17\n","[SoftImpute] Iter 81: observed MAE=0.016984 rank=17\n","[SoftImpute] Iter 82: observed MAE=0.016984 rank=17\n","[SoftImpute] Iter 83: observed MAE=0.016983 rank=17\n","[SoftImpute] Iter 84: observed MAE=0.016983 rank=17\n","[SoftImpute] Iter 85: observed MAE=0.016983 rank=17\n","[SoftImpute] Iter 86: observed MAE=0.016982 rank=17\n","[SoftImpute] Iter 87: observed MAE=0.016982 rank=17\n","[SoftImpute] Iter 88: observed MAE=0.016982 rank=17\n","[SoftImpute] Iter 89: observed MAE=0.016981 rank=17\n","[SoftImpute] Iter 90: observed MAE=0.016981 rank=17\n","[SoftImpute] Iter 91: observed MAE=0.016980 rank=17\n","[SoftImpute] Iter 92: observed MAE=0.016980 rank=17\n","[SoftImpute] Iter 93: observed MAE=0.016980 rank=17\n","[SoftImpute] Iter 94: observed MAE=0.016979 rank=17\n","[SoftImpute] Iter 95: observed MAE=0.016979 rank=17\n","[SoftImpute] Iter 96: observed MAE=0.016979 rank=17\n","[SoftImpute] Iter 97: observed MAE=0.016978 rank=17\n","[SoftImpute] Iter 98: observed MAE=0.016978 rank=17\n","[SoftImpute] Iter 99: observed MAE=0.016978 rank=17\n","[SoftImpute] Iter 100: observed MAE=0.016978 rank=17\n","[SoftImpute] Stopped after iteration 100 for lambda=0.272764\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 36029\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 21913, constraints m = 28601\n","Cones:\tprimal zero / dual free vars: 3344\n","\tlinear vars: 10032\n","\tsd vars: 15225, sd blks: 1\n","Setup time: 2.63e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.80e+21  1.73e+21  1.00e+00 -2.11e+23  4.52e+22  7.15e+22  1.94e-02 \n","   100| 1.70e-03  2.32e-03  5.64e-05  4.39e+01  4.39e+01  6.95e-15  2.40e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.40e+00s\n","\tLin-sys: nnz in L factor: 88585, avg solve time: 6.21e-04s\n","\tCones: avg projection time: 1.53e-02s\n","\tAcceleration: avg step time: 6.53e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2892e-09, dist(y, K*) = 7.8595e-09, s'y/|s||y| = 1.5617e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.7269e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.2682e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 4.1205e-04\n","----------------------------------------------------------------------------\n","c'x = 43.8925, -b'y = 43.8559\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.18698782, 0.2111195 , 0.19932045, 0.17790194, 0.17790194,\n","       0.17325078, 0.39881343])"]},"metadata":{"tags":[]},"execution_count":14}]},{"cell_type":"code","metadata":{"id":"IvIRhYplBv35","executionInfo":{"status":"ok","timestamp":1591370853073,"user_tz":300,"elapsed":113653,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"413429fe-6fa8-48d2-9924-29c0da665ffe","colab":{"base_uri":"https://localhost:8080/","height":118}},"source":["parkinson = np.vstack((res_20,res_30,res_40))\n","parkinson"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[0.14596295, 0.15959932, 0.1824323 , 0.17788684, 0.18233162,\n","        0.18697775, 0.20164826],\n","       [0.15214437, 0.18730494, 0.19012383, 0.18233666, 0.16837813,\n","        0.20116279, 0.29585588],\n","       [0.18698782, 0.2111195 , 0.19932045, 0.17790194, 0.17790194,\n","        0.17325078, 0.39881343]])"]},"metadata":{"tags":[]},"execution_count":15}]},{"cell_type":"markdown","metadata":{"id":"s1Fx2Xvso7Cr"},"source":["### 50%"]},{"cell_type":"code","metadata":{"id":"BBCsmN79o9bS","executionInfo":{"status":"ok","timestamp":1604555074727,"user_tz":360,"elapsed":42846,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"b0993f35-17c6-4363-b6cb-fc4fa0c0c4ba","colab":{"base_uri":"https://localhost:8080/"}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),30,25,20],\n","                  [sum(ytrain==1),50,40,30]])\n","    p = np.array([5,7,8,22])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,2) for k in np.arange(5)]\n","res_50 = np.mean(np.asarray(res), axis=0)\n","res_50"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 12.050453\n","[SoftImpute] Iter 1: observed MAE=0.016972 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.016956 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.016948 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.016950 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.016955 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.016962 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.016974 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.016937 rank=16\n","[SoftImpute] Iter 9: observed MAE=0.016856 rank=16\n","[SoftImpute] Iter 10: observed MAE=0.016808 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.016775 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.016754 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.016743 rank=16\n","[SoftImpute] Iter 14: observed MAE=0.016737 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.016734 rank=16\n","[SoftImpute] Iter 16: observed MAE=0.016732 rank=16\n","[SoftImpute] Iter 17: observed MAE=0.016731 rank=16\n","[SoftImpute] Iter 18: observed MAE=0.016731 rank=16\n","[SoftImpute] Iter 19: observed MAE=0.016730 rank=16\n","[SoftImpute] Iter 20: observed MAE=0.016730 rank=16\n","[SoftImpute] Iter 21: observed MAE=0.016730 rank=16\n","[SoftImpute] Iter 22: observed MAE=0.016730 rank=16\n","[SoftImpute] Iter 23: observed MAE=0.016730 rank=16\n","[SoftImpute] Iter 24: observed MAE=0.016729 rank=16\n","[SoftImpute] Iter 25: observed MAE=0.016729 rank=16\n","[SoftImpute] Iter 26: observed MAE=0.016728 rank=16\n","[SoftImpute] Iter 27: observed MAE=0.016728 rank=16\n","[SoftImpute] Iter 28: observed MAE=0.016729 rank=16\n","[SoftImpute] Iter 29: observed MAE=0.016729 rank=16\n","[SoftImpute] Iter 30: observed MAE=0.016729 rank=16\n","[SoftImpute] Iter 31: observed MAE=0.016729 rank=16\n","[SoftImpute] Iter 32: observed MAE=0.016729 rank=16\n","[SoftImpute] Iter 33: observed MAE=0.016729 rank=16\n","[SoftImpute] 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rank=16\n","[SoftImpute] Iter 52: observed MAE=0.016740 rank=16\n","[SoftImpute] Iter 53: observed MAE=0.016741 rank=16\n","[SoftImpute] Iter 54: observed MAE=0.016741 rank=16\n","[SoftImpute] Iter 55: observed MAE=0.016742 rank=16\n","[SoftImpute] Iter 56: observed MAE=0.016742 rank=16\n","[SoftImpute] Iter 57: observed MAE=0.016743 rank=16\n","[SoftImpute] Iter 58: observed MAE=0.016743 rank=16\n","[SoftImpute] Iter 59: observed MAE=0.016744 rank=16\n","[SoftImpute] Iter 60: observed MAE=0.016744 rank=16\n","[SoftImpute] Iter 61: observed MAE=0.016744 rank=16\n","[SoftImpute] Iter 62: observed MAE=0.016745 rank=16\n","[SoftImpute] Iter 63: observed MAE=0.016745 rank=16\n","[SoftImpute] Iter 64: observed MAE=0.016745 rank=16\n","[SoftImpute] Iter 65: observed MAE=0.016746 rank=16\n","[SoftImpute] Iter 66: observed MAE=0.016746 rank=16\n","[SoftImpute] Iter 67: observed MAE=0.016746 rank=16\n","[SoftImpute] Iter 68: observed MAE=0.016747 rank=16\n","[SoftImpute] Iter 69: observed 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observed MAE=0.016752 rank=16\n","[SoftImpute] Iter 88: observed MAE=0.016753 rank=16\n","[SoftImpute] Iter 89: observed MAE=0.016753 rank=16\n","[SoftImpute] Iter 90: observed MAE=0.016753 rank=16\n","[SoftImpute] Iter 91: observed MAE=0.016753 rank=16\n","[SoftImpute] Iter 92: observed MAE=0.016754 rank=16\n","[SoftImpute] Iter 93: observed MAE=0.016754 rank=16\n","[SoftImpute] Iter 94: observed MAE=0.016754 rank=16\n","[SoftImpute] Iter 95: observed MAE=0.016754 rank=16\n","[SoftImpute] Iter 96: observed MAE=0.016755 rank=16\n","[SoftImpute] Iter 97: observed MAE=0.016755 rank=16\n","[SoftImpute] Iter 98: observed MAE=0.016755 rank=16\n","[SoftImpute] Iter 99: observed MAE=0.016755 rank=16\n","[SoftImpute] Iter 100: observed MAE=0.016755 rank=16\n","[SoftImpute] Stopped after iteration 100 for lambda=0.241009\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 35021\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 21695, constraints m = 28339\n","Cones:\tprimal zero / dual free vars: 3322\n","\tlinear vars: 9966\n","\tsd vars: 15051, sd blks: 1\n","Setup time: 3.03e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.80e+21  1.74e+21  1.00e+00 -1.93e+23  4.13e+22  6.30e+22  2.19e-02 \n","   100| 1.12e-03  1.57e-03  7.71e-05  3.99e+01  3.99e+01  9.44e-15  2.44e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.44e+00s\n","\tLin-sys: nnz in L factor: 86735, avg solve time: 6.30e-04s\n","\tCones: avg projection time: 1.52e-02s\n","\tAcceleration: avg step time: 6.86e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3821e-09, dist(y, K*) = 3.0032e-09, s'y/|s||y| = -8.7677e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.0954e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 7.0328e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.1437e-04\n","----------------------------------------------------------------------------\n","c'x = 39.8739, -b'y = 39.8647\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 12.303264\n","[SoftImpute] Iter 1: observed MAE=0.017312 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.017280 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.017281 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.017289 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.017297 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.017305 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.017314 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.017327 rank=17\n","[SoftImpute] Iter 9: observed MAE=0.017305 rank=16\n","[SoftImpute] Iter 10: observed MAE=0.017223 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.017167 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.017135 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.017116 rank=16\n","[SoftImpute] Iter 14: observed MAE=0.017104 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.017097 rank=16\n","[SoftImpute] Iter 16: observed MAE=0.017093 rank=16\n","[SoftImpute] Iter 17: observed MAE=0.017090 rank=16\n","[SoftImpute] Iter 18: observed MAE=0.017090 rank=16\n","[SoftImpute] Iter 19: observed MAE=0.017089 rank=16\n","[SoftImpute] Iter 20: observed MAE=0.017089 rank=16\n","[SoftImpute] Iter 21: observed MAE=0.017089 rank=16\n","[SoftImpute] Iter 22: observed MAE=0.017090 rank=16\n","[SoftImpute] Iter 23: observed MAE=0.017090 rank=16\n","[SoftImpute] Iter 24: observed MAE=0.017091 rank=16\n","[SoftImpute] Iter 25: observed MAE=0.017091 rank=16\n","[SoftImpute] Iter 26: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 27: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 28: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 29: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 30: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 31: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 32: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 33: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 34: observed MAE=0.017093 rank=16\n","[SoftImpute] Iter 35: observed MAE=0.017093 rank=16\n","[SoftImpute] Iter 36: observed MAE=0.017093 rank=16\n","[SoftImpute] Iter 37: observed MAE=0.017094 rank=16\n","[SoftImpute] Iter 38: observed MAE=0.017094 rank=16\n","[SoftImpute] Iter 39: observed MAE=0.017094 rank=16\n","[SoftImpute] Iter 40: observed MAE=0.017094 rank=16\n","[SoftImpute] Iter 41: observed MAE=0.017094 rank=16\n","[SoftImpute] Iter 42: observed MAE=0.017094 rank=16\n","[SoftImpute] Iter 43: observed MAE=0.017095 rank=16\n","[SoftImpute] Iter 44: observed MAE=0.017095 rank=16\n","[SoftImpute] Iter 45: observed MAE=0.017095 rank=16\n","[SoftImpute] Iter 46: observed MAE=0.017096 rank=16\n","[SoftImpute] Iter 47: observed MAE=0.017096 rank=16\n","[SoftImpute] Iter 48: observed MAE=0.017096 rank=16\n","[SoftImpute] Iter 49: observed MAE=0.017096 rank=16\n","[SoftImpute] Iter 50: observed MAE=0.017096 rank=16\n","[SoftImpute] Iter 51: observed 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Iter 87: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 88: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 89: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 90: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 91: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 92: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 93: observed MAE=0.017092 rank=16\n","[SoftImpute] Iter 94: observed MAE=0.017091 rank=16\n","[SoftImpute] Iter 95: observed MAE=0.017091 rank=16\n","[SoftImpute] Iter 96: observed MAE=0.017091 rank=16\n","[SoftImpute] Iter 97: observed MAE=0.017091 rank=16\n","[SoftImpute] Iter 98: observed MAE=0.017091 rank=16\n","[SoftImpute] Iter 99: observed MAE=0.017091 rank=16\n","[SoftImpute] Iter 100: observed MAE=0.017091 rank=16\n","[SoftImpute] Stopped after iteration 100 for lambda=0.246065\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 35610\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 22132, constraints m = 28864\n","Cones:\tprimal zero / dual free vars: 3366\n","\tlinear vars: 10098\n","\tsd vars: 15400, sd blks: 1\n","Setup time: 3.03e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.82e+21  1.76e+21  1.00e+00 -2.00e+23  4.28e+22  6.51e+22  2.09e-02 \n","   100| 1.06e-03  1.32e-03  4.13e-05  4.05e+01  4.05e+01  2.13e-15  2.40e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.40e+00s\n","\tLin-sys: nnz in L factor: 88296, avg solve time: 6.24e-04s\n","\tCones: avg projection time: 1.49e-02s\n","\tAcceleration: avg step time: 6.78e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.4389e-09, dist(y, K*) = 3.5452e-09, s'y/|s||y| = 1.0445e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.2465e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 7.6222e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.6271e-05\n","----------------------------------------------------------------------------\n","c'x = 40.4851, -b'y = 40.4864\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 12.308885\n","[SoftImpute] Iter 1: observed MAE=0.016836 rank=18\n","[SoftImpute] Iter 2: observed MAE=0.016772 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.016755 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.016758 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.016771 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.016786 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.016802 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.016822 rank=17\n","[SoftImpute] Iter 9: observed MAE=0.016843 rank=17\n","[SoftImpute] Iter 10: observed MAE=0.016862 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.016784 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.016740 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.016707 rank=16\n","[SoftImpute] Iter 14: observed MAE=0.016682 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.016663 rank=16\n","[SoftImpute] Iter 16: observed MAE=0.016650 rank=16\n","[SoftImpute] Iter 17: observed MAE=0.016641 rank=16\n","[SoftImpute] Iter 18: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 19: observed MAE=0.016632 rank=16\n","[SoftImpute] Iter 20: observed MAE=0.016629 rank=16\n","[SoftImpute] Iter 21: observed 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rank=16\n","[SoftImpute] Iter 75: observed MAE=0.016636 rank=16\n","[SoftImpute] Iter 76: observed MAE=0.016636 rank=16\n","[SoftImpute] Iter 77: observed MAE=0.016636 rank=16\n","[SoftImpute] Iter 78: observed MAE=0.016636 rank=16\n","[SoftImpute] Iter 79: observed MAE=0.016636 rank=16\n","[SoftImpute] Iter 80: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 81: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 82: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 83: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 84: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 85: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 86: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 87: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 88: observed MAE=0.016635 rank=16\n","[SoftImpute] Iter 89: observed MAE=0.016634 rank=16\n","[SoftImpute] Iter 90: observed MAE=0.016634 rank=16\n","[SoftImpute] Iter 91: observed MAE=0.016634 rank=16\n","[SoftImpute] Iter 92: observed MAE=0.016634 rank=16\n","[SoftImpute] Iter 93: observed MAE=0.016634 rank=16\n","[SoftImpute] Iter 94: observed MAE=0.016634 rank=16\n","[SoftImpute] Iter 95: observed MAE=0.016634 rank=16\n","[SoftImpute] Iter 96: observed MAE=0.016634 rank=16\n","[SoftImpute] Iter 97: observed MAE=0.016633 rank=16\n","[SoftImpute] Iter 98: observed MAE=0.016633 rank=16\n","[SoftImpute] Iter 99: observed MAE=0.016633 rank=16\n","[SoftImpute] Iter 100: observed MAE=0.016633 rank=16\n","[SoftImpute] Stopped after iteration 100 for lambda=0.246178\n"],"name":"stdout"},{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/impute/_iterative.py:638: ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 38310\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 24148, constraints m = 31276\n","Cones:\tprimal zero / dual free vars: 3564\n","\tlinear vars: 10692\n","\tsd vars: 17020, sd blks: 1\n","Setup time: 3.09e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.91e+21  1.84e+21  1.00e+00 -2.17e+23  4.61e+22  6.95e+22  2.42e-02 \n","   100| 6.99e-04  8.52e-04  2.23e-04  4.09e+01  4.09e+01  4.41e-15  2.60e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.60e+00s\n","\tLin-sys: nnz in L factor: 95469, avg solve time: 6.86e-04s\n","\tCones: avg projection time: 1.60e-02s\n","\tAcceleration: avg step time: 7.35e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3643e-09, dist(y, K*) = 2.3425e-09, s'y/|s||y| = 5.9113e-15\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.9852e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 8.5223e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.2268e-04\n","----------------------------------------------------------------------------\n","c'x = 40.9298, -b'y = 40.9482\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 12.381802\n","[SoftImpute] Iter 1: observed MAE=0.017113 rank=18\n","[SoftImpute] Iter 2: observed MAE=0.017103 rank=18\n","[SoftImpute] Iter 3: observed MAE=0.017081 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.017051 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.017037 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.017029 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.017025 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.017021 rank=17\n","[SoftImpute] Iter 9: observed MAE=0.017016 rank=17\n","[SoftImpute] Iter 10: observed MAE=0.017013 rank=17\n","[SoftImpute] Iter 11: observed MAE=0.017010 rank=17\n","[SoftImpute] Iter 12: observed MAE=0.017008 rank=17\n","[SoftImpute] Iter 13: observed MAE=0.017005 rank=17\n","[SoftImpute] Iter 14: observed MAE=0.016993 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.016919 rank=16\n","[SoftImpute] Iter 16: observed MAE=0.016875 rank=16\n","[SoftImpute] Iter 17: observed MAE=0.016847 rank=16\n","[SoftImpute] Iter 18: observed MAE=0.016829 rank=16\n","[SoftImpute] Iter 19: observed MAE=0.016817 rank=16\n","[SoftImpute] Iter 20: observed MAE=0.016808 rank=16\n","[SoftImpute] Iter 21: observed 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observed MAE=0.016771 rank=16\n","[SoftImpute] Iter 40: observed MAE=0.016771 rank=16\n","[SoftImpute] Iter 41: observed MAE=0.016770 rank=16\n","[SoftImpute] Iter 42: observed MAE=0.016769 rank=16\n","[SoftImpute] Iter 43: observed MAE=0.016769 rank=16\n","[SoftImpute] Iter 44: observed MAE=0.016768 rank=16\n","[SoftImpute] Iter 45: observed MAE=0.016768 rank=16\n","[SoftImpute] Iter 46: observed MAE=0.016767 rank=16\n","[SoftImpute] Iter 47: observed MAE=0.016767 rank=16\n","[SoftImpute] Iter 48: observed MAE=0.016767 rank=16\n","[SoftImpute] Iter 49: observed MAE=0.016767 rank=16\n","[SoftImpute] Iter 50: observed MAE=0.016767 rank=16\n","[SoftImpute] Iter 51: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 52: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 53: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 54: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 55: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 56: observed MAE=0.016766 rank=16\n","[SoftImpute] 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rank=16\n","[SoftImpute] Iter 75: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 76: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 77: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 78: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 79: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 80: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 81: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 82: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 83: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 84: observed MAE=0.016766 rank=16\n","[SoftImpute] Iter 85: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 86: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 87: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 88: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 89: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 90: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 91: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 92: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 93: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 94: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 95: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 96: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 97: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 98: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 99: observed MAE=0.016765 rank=16\n","[SoftImpute] Iter 100: observed MAE=0.016765 rank=16\n","[SoftImpute] Stopped after iteration 100 for lambda=0.247636\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 38310\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 24148, constraints m = 31276\n","Cones:\tprimal zero / dual free vars: 3564\n","\tlinear vars: 10692\n","\tsd vars: 17020, sd blks: 1\n","Setup time: 3.98e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.91e+21  1.84e+21  1.00e+00 -2.17e+23  4.61e+22  6.95e+22  2.29e-02 \n","   100| 7.92e-04  8.46e-04  1.94e-04  4.14e+01  4.14e+01  1.83e-14  2.62e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.62e+00s\n","\tLin-sys: nnz in L factor: 95469, avg solve time: 6.80e-04s\n","\tCones: avg projection time: 1.59e-02s\n","\tAcceleration: avg step time: 7.75e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.5842e-09, dist(y, K*) = 4.4681e-09, s'y/|s||y| = 4.3588e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.4169e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 6.7850e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.4058e-04\n","----------------------------------------------------------------------------\n","c'x = 41.3369, -b'y = 41.3084\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 12.468486\n","[SoftImpute] Iter 1: observed MAE=0.017312 rank=17\n","[SoftImpute] Iter 2: observed MAE=0.017306 rank=17\n","[SoftImpute] Iter 3: observed MAE=0.017316 rank=17\n","[SoftImpute] Iter 4: observed MAE=0.017327 rank=17\n","[SoftImpute] Iter 5: observed MAE=0.017337 rank=17\n","[SoftImpute] Iter 6: observed MAE=0.017346 rank=17\n","[SoftImpute] Iter 7: observed MAE=0.017354 rank=17\n","[SoftImpute] Iter 8: observed MAE=0.017360 rank=17\n","[SoftImpute] Iter 9: observed MAE=0.017372 rank=17\n","[SoftImpute] Iter 10: observed MAE=0.017349 rank=16\n","[SoftImpute] Iter 11: observed MAE=0.017280 rank=16\n","[SoftImpute] Iter 12: observed MAE=0.017229 rank=16\n","[SoftImpute] Iter 13: observed MAE=0.017197 rank=16\n","[SoftImpute] Iter 14: observed MAE=0.017176 rank=16\n","[SoftImpute] Iter 15: observed MAE=0.017162 rank=16\n","[SoftImpute] Iter 16: observed MAE=0.017154 rank=16\n","[SoftImpute] Iter 17: observed MAE=0.017149 rank=16\n","[SoftImpute] Iter 18: observed MAE=0.017147 rank=16\n","[SoftImpute] Iter 19: observed MAE=0.017145 rank=16\n","[SoftImpute] Iter 20: observed MAE=0.017144 rank=16\n","[SoftImpute] Iter 21: observed MAE=0.017144 rank=16\n","[SoftImpute] Iter 22: observed MAE=0.017143 rank=16\n","[SoftImpute] Iter 23: observed MAE=0.017143 rank=16\n","[SoftImpute] Iter 24: observed MAE=0.017143 rank=16\n","[SoftImpute] Iter 25: observed 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rank=16\n","[SoftImpute] Iter 79: observed MAE=0.017128 rank=16\n","[SoftImpute] Iter 80: observed MAE=0.017128 rank=16\n","[SoftImpute] Iter 81: observed MAE=0.017128 rank=16\n","[SoftImpute] Iter 82: observed MAE=0.017128 rank=16\n","[SoftImpute] Iter 83: observed MAE=0.017128 rank=16\n","[SoftImpute] Iter 84: observed MAE=0.017128 rank=16\n","[SoftImpute] Iter 85: observed MAE=0.017127 rank=16\n","[SoftImpute] Iter 86: observed MAE=0.017127 rank=16\n","[SoftImpute] Iter 87: observed MAE=0.017127 rank=16\n","[SoftImpute] Iter 88: observed MAE=0.017127 rank=16\n","[SoftImpute] Iter 89: observed MAE=0.017127 rank=16\n","[SoftImpute] Iter 90: observed MAE=0.017127 rank=16\n","[SoftImpute] Iter 91: observed MAE=0.017126 rank=16\n","[SoftImpute] Iter 92: observed MAE=0.017126 rank=16\n","[SoftImpute] Iter 93: observed MAE=0.017126 rank=16\n","[SoftImpute] Iter 94: observed MAE=0.017126 rank=16\n","[SoftImpute] Iter 95: observed MAE=0.017126 rank=16\n","[SoftImpute] Iter 96: observed MAE=0.017126 rank=16\n","[SoftImpute] Iter 97: observed MAE=0.017126 rank=16\n","[SoftImpute] Iter 98: observed MAE=0.017126 rank=16\n","[SoftImpute] Iter 99: observed MAE=0.017126 rank=16\n","[SoftImpute] Iter 100: observed MAE=0.017126 rank=16\n","[SoftImpute] Stopped after iteration 100 for lambda=0.249370\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 35315\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 21913, constraints m = 28601\n","Cones:\tprimal zero / dual free vars: 3344\n","\tlinear vars: 10032\n","\tsd vars: 15225, sd blks: 1\n","Setup time: 3.58e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.81e+21  1.75e+21  1.00e+00 -2.01e+23  4.29e+22  6.54e+22  2.01e-02 \n","   100| 2.41e-03  3.55e-03  9.92e-04  4.13e+01  4.12e+01  5.13e-15  2.38e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.38e+00s\n","\tLin-sys: nnz in L factor: 87514, avg solve time: 6.15e-04s\n","\tCones: avg projection time: 1.49e-02s\n","\tAcceleration: avg step time: 6.58e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3384e-09, dist(y, K*) = 2.7077e-09, s'y/|s||y| = 7.0962e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.8246e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.5718e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.2386e-04\n","----------------------------------------------------------------------------\n","c'x = 41.2687, -b'y = 41.2500\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.27657304, 0.36153227, 0.32495218, 0.38956005, 0.21123024,\n","       0.3939998 , 0.50293765])"]},"metadata":{"tags":[]},"execution_count":29}]},{"cell_type":"code","metadata":{"id":"QdEJ0yaK75bG"},"source":[""],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"-VB9LJW3IOPk"},"source":["# wine\n","The data set is also available in sklearn, as noted in the package's website. So, we load it directly from sklearn"]},{"cell_type":"code","metadata":{"id":"zgmq0y4yIOPm","executionInfo":{"status":"ok","timestamp":1604555319623,"user_tz":360,"elapsed":724,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"1cf7707f-9903-4f67-bacc-7f81a9bcc9be","colab":{"base_uri":"https://localhost:8080/"}},"source":["wine = datasets.load_wine()\n","X,y = wine.data, wine.target.ravel() \n","print(sum(y==0), sum(y==1), sum(y==2))"],"execution_count":null,"outputs":[{"output_type":"stream","text":["59 71 48\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"J3Ptx_6Ce10t"},"source":["## 20%"]},{"cell_type":"code","metadata":{"id":"YoG6jFRHIOPv","executionInfo":{"status":"ok","timestamp":1591370868386,"user_tz":300,"elapsed":123601,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"6a2f6bd3-8130-4e34-a09b-401b9b62ff0d","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),40,35,27], [sum(ytrain==1),45,40,35],\n","                  [sum(ytrain==2),30,25,22]])\n","    p = np.array([5,7,9,13])   \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res20 = np.mean(np.asarray(res), axis=0)\n","res20"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 16.079100\n","[SoftImpute] Iter 1: observed MAE=0.022542 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022609 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022663 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022707 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022745 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022779 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022808 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022832 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022852 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022869 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022885 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022900 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022912 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022924 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022934 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022942 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022950 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022958 rank=13\n","[SoftImpute] Iter 19: observed 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rank=13\n","[SoftImpute] Iter 73: observed MAE=0.023199 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.023199 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.023200 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.023201 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.023201 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.023202 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.023202 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.023203 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.023203 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.023204 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.023204 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.023204 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.023205 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.023205 rank=13\n","[SoftImpute] Stopped after iteration 86 for lambda=0.321582\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23358\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15064, constraints m = 18652\n","Cones:\tprimal zero / dual free vars: 1794\n","\tlinear vars: 5382\n","\tsd vars: 11476, sd blks: 1\n","Setup time: 2.22e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.50e+21  1.41e+21  1.00e+00 -1.81e+23  3.67e+22  5.90e+22  1.66e-02 \n","   100| 4.96e-04  6.95e-04  9.32e-05  4.07e+01  4.07e+01  1.24e-14  1.79e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.79e+00s\n","\tLin-sys: nnz in L factor: 58530, avg solve time: 4.32e-04s\n","\tCones: avg projection time: 1.21e-02s\n","\tAcceleration: avg step time: 4.32e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6655e-09, dist(y, K*) = 1.3863e-09, s'y/|s||y| = 4.7213e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.6545e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 5.9280e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.6812e-04\n","----------------------------------------------------------------------------\n","c'x = 40.7435, -b'y = 40.7296\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 15.732221\n","[SoftImpute] Iter 1: observed MAE=0.021936 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022000 rank=13\n","[SoftImpute] Iter 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lambda=0.314644\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23358\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15064, constraints m = 18652\n","Cones:\tprimal zero / dual free vars: 1794\n","\tlinear vars: 5382\n","\tsd vars: 11476, sd blks: 1\n","Setup time: 2.18e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.50e+21  1.41e+21  1.00e+00 -1.77e+23  3.60e+22  5.78e+22  1.54e-02 \n","   100| 1.24e-03  1.32e-03  1.46e-04  4.02e+01  4.02e+01  5.92e-15  1.78e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.78e+00s\n","\tLin-sys: nnz in L factor: 58530, avg solve time: 4.31e-04s\n","\tCones: avg projection time: 1.21e-02s\n","\tAcceleration: avg step time: 4.22e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2480e-09, dist(y, K*) = 2.6959e-09, s'y/|s||y| = -9.3170e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.5112e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.5628e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.0498e-04\n","----------------------------------------------------------------------------\n","c'x = 40.2330, -b'y = 40.2245\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 16.535984\n","[SoftImpute] Iter 1: observed MAE=0.022815 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022876 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022928 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022974 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.023013 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.023046 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.023074 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.023099 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.023121 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.023140 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.023157 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.023172 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.023185 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.023197 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.023207 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.023216 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.023225 rank=13\n","[SoftImpute] Iter 18: 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rank=13\n","[SoftImpute] Iter 54: observed MAE=0.023443 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.023445 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.023447 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.023449 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.023451 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.023453 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.023455 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.023456 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.023458 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.023459 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.023461 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.023462 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.023463 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.023464 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.023465 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.023466 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.023467 rank=13\n","[SoftImpute] Iter 71: observed 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observed MAE=0.023478 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.023478 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.023479 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.023479 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.023479 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.023479 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.023480 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.023480 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.023480 rank=13\n","[SoftImpute] Stopped after iteration 97 for lambda=0.330720\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 25437\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 16702, constraints m = 20524\n","Cones:\tprimal zero / dual free vars: 1911\n","\tlinear vars: 5733\n","\tsd vars: 12880, sd blks: 1\n","Setup time: 2.35e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.59e+21  1.49e+21  1.00e+00 -2.03e+23  4.09e+22  6.48e+22  1.67e-02 \n","   100| 1.22e-03  1.54e-03  4.25e-04  4.17e+01  4.17e+01  6.89e-16  1.90e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.90e+00s\n","\tLin-sys: nnz in L factor: 64164, avg solve time: 4.91e-04s\n","\tCones: avg projection time: 1.24e-02s\n","\tAcceleration: avg step time: 4.92e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.8492e-09, dist(y, K*) = 2.9619e-09, s'y/|s||y| = -1.0364e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.8018e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.3383e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 4.1549e-04\n","----------------------------------------------------------------------------\n","c'x = 41.7429, -b'y = 41.7078\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 16.421862\n","[SoftImpute] Iter 1: observed MAE=0.022485 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022540 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022586 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022628 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022666 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022700 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022729 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022755 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022778 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022798 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022816 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022833 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022849 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022864 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022876 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022888 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022898 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022907 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.022916 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.022924 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.022932 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.022940 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.022949 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.022958 rank=13\n","[SoftImpute] Iter 25: observed 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observed MAE=0.023091 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.023096 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.023100 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.023105 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.023109 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.023113 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.023117 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.023121 rank=13\n","[SoftImpute] Iter 51: observed MAE=0.023124 rank=13\n","[SoftImpute] Iter 52: observed MAE=0.023128 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.023131 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.023134 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.023137 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.023141 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.023143 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.023146 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.023149 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.023151 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.023153 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.023155 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.023157 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.023159 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.023161 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.023163 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.023164 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.023166 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.023167 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.023169 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.023170 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.023171 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.023172 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.023173 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.023175 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.023176 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.023176 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.023177 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.023178 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.023179 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.023180 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.023181 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.023181 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.023182 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.023183 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.023183 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.023184 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.023184 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.023185 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.023186 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.023186 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.023187 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.023187 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.023187 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.023188 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.023188 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.023189 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.023189 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.023189 rank=13\n","[SoftImpute] Stopped after iteration 99 for lambda=0.328437\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 26148\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17266, constraints m = 21166\n","Cones:\tprimal zero / dual free vars: 1950\n","\tlinear vars: 5850\n","\tsd vars: 13366, sd blks: 1\n","Setup time: 2.41e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.62e+21  1.52e+21  1.00e+00 -2.08e+23  4.19e+22  6.59e+22  1.91e-02 \n","   100| 2.74e-03  4.05e-03  1.10e-04  4.18e+01  4.18e+01  2.35e-14  2.01e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.01e+00s\n","\tLin-sys: nnz in L factor: 66096, avg solve time: 4.85e-04s\n","\tCones: avg projection time: 1.37e-02s\n","\tAcceleration: avg step time: 4.74e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6378e-09, dist(y, K*) = 2.8629e-09, s'y/|s||y| = -4.0145e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.8474e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.3456e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 4.2029e-05\n","----------------------------------------------------------------------------\n","c'x = 41.7603, -b'y = 41.7568\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 15.966388\n","[SoftImpute] Iter 1: observed MAE=0.022276 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022333 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022382 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022423 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022459 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022488 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022513 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022535 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022556 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022574 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022591 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022607 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022621 rank=13\n","[SoftImpute] 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rank=13\n","[SoftImpute] Iter 32: observed MAE=0.022786 rank=13\n","[SoftImpute] Iter 33: observed MAE=0.022792 rank=13\n","[SoftImpute] Iter 34: observed MAE=0.022799 rank=13\n","[SoftImpute] Iter 35: observed MAE=0.022806 rank=13\n","[SoftImpute] Iter 36: observed MAE=0.022813 rank=13\n","[SoftImpute] Iter 37: observed MAE=0.022819 rank=13\n","[SoftImpute] Iter 38: observed MAE=0.022824 rank=13\n","[SoftImpute] Iter 39: observed MAE=0.022830 rank=13\n","[SoftImpute] Iter 40: observed MAE=0.022835 rank=13\n","[SoftImpute] Iter 41: observed MAE=0.022841 rank=13\n","[SoftImpute] Iter 42: observed MAE=0.022846 rank=13\n","[SoftImpute] Iter 43: observed MAE=0.022850 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.022855 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.022859 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.022863 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.022867 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.022870 rank=13\n","[SoftImpute] Iter 49: observed 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observed MAE=0.022906 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.022907 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.022908 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022910 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022910 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022911 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022912 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022913 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022914 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022914 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022915 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022916 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022916 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022917 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022917 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022918 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022918 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022918 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022919 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022919 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022920 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022920 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022920 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022921 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022921 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022921 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022921 rank=13\n","[SoftImpute] Stopped after iteration 93 for lambda=0.319328\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23585\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15242, constraints m = 18856\n","Cones:\tprimal zero / dual free vars: 1807\n","\tlinear vars: 5421\n","\tsd vars: 11628, sd blks: 1\n","Setup time: 1.86e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.51e+21  1.42e+21  1.00e+00 -1.82e+23  3.70e+22  5.93e+22  1.70e-02 \n","   100| 1.61e-03  1.98e-03  4.22e-04  4.14e+01  4.15e+01  9.57e-15  1.77e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.77e+00s\n","\tLin-sys: nnz in L factor: 59144, avg solve time: 4.29e-04s\n","\tCones: avg projection time: 1.19e-02s\n","\tAcceleration: avg step time: 4.26e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7502e-09, dist(y, K*) = 1.9334e-08, s'y/|s||y| = -1.1194e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.9646e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.2109e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.8114e-04\n","----------------------------------------------------------------------------\n","c'x = 41.3322, -b'y = 41.3087\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.01145161, 0.02504608, 0.01790323, 0.01290323, 0.03004608,\n","       0.01290323, 0.20108013])"]},"metadata":{"tags":[]},"execution_count":17}]},{"cell_type":"markdown","metadata":{"id":"-mbA9aOCfEaX"},"source":["## 30%"]},{"cell_type":"code","metadata":{"id":"IzTn4cIzJ2Ua","executionInfo":{"status":"ok","timestamp":1591370885304,"user_tz":300,"elapsed":138619,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"bcb2db3e-a8bc-4b21-a111-bdcd5f79b32d","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),40,35,25], [sum(ytrain==1),45,40,30],\n","                  [sum(ytrain==2),35,25,22]])\n","    p = np.array([2,4,7,13])  \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res30 = np.mean(np.asarray(res), axis=0)\n","res30"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 15.206606\n","[SoftImpute] Iter 1: observed MAE=0.022682 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022728 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022769 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022805 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022838 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022868 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022896 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022923 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022947 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022969 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022987 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.023004 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.023019 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.023032 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.023044 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.023055 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.023065 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.023074 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.023083 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.023091 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.023098 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.023105 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.023112 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.023119 rank=13\n","[SoftImpute] Iter 25: observed MAE=0.023125 rank=13\n","[SoftImpute] Iter 26: observed MAE=0.023131 rank=13\n","[SoftImpute] Iter 27: observed MAE=0.023137 rank=13\n","[SoftImpute] Iter 28: observed MAE=0.023143 rank=13\n","[SoftImpute] Iter 29: observed MAE=0.023148 rank=13\n","[SoftImpute] Iter 30: observed MAE=0.023154 rank=13\n","[SoftImpute] Iter 31: observed MAE=0.023159 rank=13\n","[SoftImpute] Iter 32: observed MAE=0.023164 rank=13\n","[SoftImpute] Iter 33: observed MAE=0.023170 rank=13\n","[SoftImpute] 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rank=13\n","[SoftImpute] Iter 52: observed MAE=0.023264 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.023268 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.023271 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.023274 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.023277 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.023280 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.023283 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.023286 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.023288 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.023290 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.023293 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.023295 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.023297 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.023299 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.023301 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.023303 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.023304 rank=13\n","[SoftImpute] Iter 69: observed 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observed MAE=0.023324 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.023325 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.023325 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.023326 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.023326 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.023327 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.023327 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.023328 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.023328 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.023329 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.023329 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.023329 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.023330 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.023330 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.304132\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23002\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15064, constraints m = 18652\n","Cones:\tprimal zero / dual free vars: 1794\n","\tlinear vars: 5382\n","\tsd vars: 11476, sd blks: 1\n","Setup time: 1.95e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.51e+21  1.42e+21  1.00e+00 -1.74e+23  3.54e+22  5.52e+22  1.63e-02 \n","   100| 1.18e-03  1.68e-03  2.75e-04  3.93e+01  3.93e+01  2.56e-15  1.74e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.74e+00s\n","\tLin-sys: nnz in L factor: 57996, avg solve time: 4.22e-04s\n","\tCones: avg projection time: 1.18e-02s\n","\tAcceleration: avg step time: 4.09e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6731e-09, dist(y, K*) = 1.3177e-09, s'y/|s||y| = -4.0641e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.1848e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.8521e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.8672e-05\n","----------------------------------------------------------------------------\n","c'x = 39.3358, -b'y = 39.3343\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 15.454885\n","[SoftImpute] Iter 1: observed MAE=0.023202 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.023246 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.023284 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.023316 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.023344 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.023370 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.023393 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.023414 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.023432 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.023447 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.023462 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.023475 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.023488 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.023502 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.023515 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.023527 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.023537 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.023548 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.023557 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.023567 rank=13\n","[SoftImpute] Iter 21: observed 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rank=13\n","[SoftImpute] Iter 75: observed MAE=0.023835 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.023837 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.023838 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.023840 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.023841 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.023842 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.023844 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.023845 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.023846 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.023847 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.023848 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.023849 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.023850 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.023851 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.023852 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.023852 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.023853 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.023854 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.023855 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.023855 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.023856 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.023857 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.023857 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.023858 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.023858 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.023859 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.309098\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23002\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15064, constraints m = 18652\n","Cones:\tprimal zero / dual free vars: 1794\n","\tlinear vars: 5382\n","\tsd vars: 11476, sd blks: 1\n","Setup time: 2.31e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.51e+21  1.42e+21  1.00e+00 -1.76e+23  3.57e+22  5.58e+22  1.73e-02 \n","   100| 1.01e-03  1.09e-03  3.29e-05  3.98e+01  3.98e+01  8.32e-15  1.73e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.73e+00s\n","\tLin-sys: nnz in L factor: 57996, avg solve time: 4.24e-04s\n","\tCones: avg projection time: 1.17e-02s\n","\tAcceleration: avg step time: 4.09e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1090e-09, dist(y, K*) = 2.1723e-09, s'y/|s||y| = -8.0325e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.9999e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.0321e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.8418e-04\n","----------------------------------------------------------------------------\n","c'x = 39.7556, -b'y = 39.7247\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 15.276504\n","[SoftImpute] Iter 1: observed MAE=0.022418 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022470 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022515 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022555 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022591 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022624 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022653 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022679 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022702 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022724 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022744 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022762 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022780 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022796 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022811 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022825 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022838 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022851 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.022862 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.022873 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.022883 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.022892 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.022900 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.022907 rank=13\n","[SoftImpute] Iter 25: observed 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observed MAE=0.022994 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.022997 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.023000 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.023002 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.023004 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.023006 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.023009 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.023011 rank=13\n","[SoftImpute] Iter 51: observed MAE=0.023014 rank=13\n","[SoftImpute] Iter 52: observed MAE=0.023016 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.023019 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.023021 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.023024 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.023026 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.023029 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.023031 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.023033 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.023035 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.023038 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.023040 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.023042 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.023044 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.023046 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.023048 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.023050 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.023052 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.023054 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.023055 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.023057 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.023059 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.023061 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.023062 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.023064 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.023065 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.023067 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.023068 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.023070 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.023071 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.023072 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.023073 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.023074 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.023076 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.023077 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.023078 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.023079 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.023080 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.023081 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.023082 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.023083 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.023084 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.023085 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.023086 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.023087 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.023088 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.023089 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.023090 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.023091 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.023091 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.305530\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 25027\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 16702, constraints m = 20524\n","Cones:\tprimal zero / dual free vars: 1911\n","\tlinear vars: 5733\n","\tsd vars: 12880, sd blks: 1\n","Setup time: 2.42e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.61e+21  1.51e+21  1.00e+00 -1.91e+23  3.85e+22  5.91e+22  1.37e-02 \n","   100| 3.90e+00  4.70e-01  9.76e-01  3.98e+01 -1.05e+00  3.60e-15  1.86e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.86e+00s\n","\tLin-sys: nnz in L factor: 63549, avg solve time: 4.65e-04s\n","\tCones: avg projection time: 1.25e-02s\n","\tAcceleration: avg step time: 4.55e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7105e-09, dist(y, K*) = 1.3375e-09, s'y/|s||y| = 3.3671e-15\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.1445e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.7870e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.6972e-05\n","----------------------------------------------------------------------------\n","c'x = 39.5122, -b'y = 39.5152\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 15.220781\n","[SoftImpute] Iter 1: observed MAE=0.022394 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022451 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022503 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022549 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022587 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022620 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022649 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022676 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022699 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022722 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022743 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022762 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022779 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022793 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022806 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022817 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022827 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022836 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.022845 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.022853 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.022860 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.022866 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.022871 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.022875 rank=13\n","[SoftImpute] Iter 25: observed MAE=0.022880 rank=13\n","[SoftImpute] Iter 26: observed MAE=0.022884 rank=13\n","[SoftImpute] Iter 27: observed MAE=0.022889 rank=13\n","[SoftImpute] Iter 28: observed MAE=0.022893 rank=13\n","[SoftImpute] Iter 29: observed MAE=0.022897 rank=13\n","[SoftImpute] Iter 30: observed MAE=0.022901 rank=13\n","[SoftImpute] Iter 31: observed MAE=0.022905 rank=13\n","[SoftImpute] Iter 32: observed MAE=0.022909 rank=13\n","[SoftImpute] Iter 33: observed MAE=0.022912 rank=13\n","[SoftImpute] Iter 34: observed MAE=0.022916 rank=13\n","[SoftImpute] Iter 35: observed MAE=0.022919 rank=13\n","[SoftImpute] Iter 36: observed MAE=0.022922 rank=13\n","[SoftImpute] Iter 37: observed MAE=0.022925 rank=13\n","[SoftImpute] Iter 38: observed MAE=0.022928 rank=13\n","[SoftImpute] Iter 39: observed MAE=0.022931 rank=13\n","[SoftImpute] Iter 40: observed MAE=0.022933 rank=13\n","[SoftImpute] Iter 41: observed MAE=0.022935 rank=13\n","[SoftImpute] Iter 42: observed MAE=0.022937 rank=13\n","[SoftImpute] Iter 43: observed MAE=0.022940 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.022942 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.022944 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.022946 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.022949 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.022951 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.022953 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.022955 rank=13\n","[SoftImpute] Iter 51: observed MAE=0.022958 rank=13\n","[SoftImpute] Iter 52: observed MAE=0.022960 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.022962 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.022964 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.022965 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.022967 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.022969 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.022971 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.022973 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.022974 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.022976 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.022977 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.022978 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.022980 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.022981 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.022982 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.022983 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.022984 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.022985 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022986 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022988 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022989 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022990 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022991 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022992 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022993 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022994 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022996 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022997 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022998 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022999 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.023000 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.023001 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.023002 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.023003 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.023004 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.023005 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.023005 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.023006 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.023007 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.023008 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.023009 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.023009 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.023010 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.023011 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.023012 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.023012 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.023013 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.023014 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.023014 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.304416\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 25720\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17266, constraints m = 21166\n","Cones:\tprimal zero / dual free vars: 1950\n","\tlinear vars: 5850\n","\tsd vars: 13366, sd blks: 1\n","Setup time: 2.38e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.64e+21  1.54e+21  1.00e+00 -1.96e+23  3.95e+22  6.02e+22  1.99e-02 \n","   100| 1.16e-03  1.73e-03  2.35e-04  3.95e+01  3.96e+01  1.69e-14  1.99e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.99e+00s\n","\tLin-sys: nnz in L factor: 65454, avg solve time: 4.78e-04s\n","\tCones: avg projection time: 1.33e-02s\n","\tAcceleration: avg step time: 4.90e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7245e-09, dist(y, K*) = 1.7256e-09, s'y/|s||y| = 5.9672e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.3452e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.5454e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.0465e-05\n","----------------------------------------------------------------------------\n","c'x = 39.5180, -b'y = 39.5204\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.984622\n","[SoftImpute] Iter 1: observed MAE=0.022337 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022380 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022417 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022448 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022476 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022504 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022530 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022553 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022574 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022593 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022612 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022631 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022648 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022664 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022678 rank=13\n","[SoftImpute] Iter 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rank=13\n","[SoftImpute] Iter 34: observed MAE=0.022806 rank=13\n","[SoftImpute] Iter 35: observed MAE=0.022809 rank=13\n","[SoftImpute] Iter 36: observed MAE=0.022812 rank=13\n","[SoftImpute] Iter 37: observed MAE=0.022815 rank=13\n","[SoftImpute] Iter 38: observed MAE=0.022818 rank=13\n","[SoftImpute] Iter 39: observed MAE=0.022822 rank=13\n","[SoftImpute] Iter 40: observed MAE=0.022825 rank=13\n","[SoftImpute] Iter 41: observed MAE=0.022828 rank=13\n","[SoftImpute] Iter 42: observed MAE=0.022830 rank=13\n","[SoftImpute] Iter 43: observed MAE=0.022833 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.022836 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.022840 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.022842 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.022845 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.022848 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.022850 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.022853 rank=13\n","[SoftImpute] Iter 51: observed MAE=0.022855 rank=13\n","[SoftImpute] Iter 52: observed MAE=0.022857 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.022860 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.022862 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.022864 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.022866 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.022868 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.022871 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.022873 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.022875 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.022877 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.022879 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.022882 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.022884 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.022886 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.022888 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.022890 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.022891 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.022893 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022895 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022896 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022898 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022899 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022901 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022903 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022904 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022905 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022907 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022908 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022909 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022911 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022912 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022913 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022914 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022915 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022916 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022917 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022918 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022919 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022920 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022920 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022921 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022922 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.022923 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.022924 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.022924 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.022925 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.022926 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.022926 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.022927 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.299692\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 23223\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15242, constraints m = 18856\n","Cones:\tprimal zero / dual free vars: 1807\n","\tlinear vars: 5421\n","\tsd vars: 11628, sd blks: 1\n","Setup time: 2.08e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.52e+21  1.43e+21  1.00e+00 -1.74e+23  3.52e+22  5.49e+22  1.56e-02 \n","   100| 2.41e-03  3.40e-03  9.53e-05  3.94e+01  3.95e+01  1.71e-14  1.76e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.76e+00s\n","\tLin-sys: nnz in L factor: 58601, avg solve time: 4.27e-04s\n","\tCones: avg projection time: 1.19e-02s\n","\tAcceleration: avg step time: 4.19e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6259e-09, dist(y, K*) = 1.8723e-09, s'y/|s||y| = 4.3570e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.5109e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.5501e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.4109e-04\n","----------------------------------------------------------------------------\n","c'x = 39.4444, -b'y = 39.4252\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.01145161, 0.0414977 , 0.01790323, 0.01645161, 0.05175411,\n","       0.01645161, 0.30420463])"]},"metadata":{"tags":[]},"execution_count":18}]},{"cell_type":"markdown","metadata":{"id":"JJv8_6hJfKcT"},"source":["## 40%"]},{"cell_type":"code","metadata":{"id":"WkTgwR-QMGzH","executionInfo":{"status":"ok","timestamp":1591370902053,"user_tz":300,"elapsed":153535,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"63d0188c-db93-4039-e646-936ba927e5cf","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),30,25,20], [sum(ytrain==1),35,27,24],\n","                  [sum(ytrain==2),26,22,20]])\n","    p = np.array([2,5,9,13])  \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res40 = np.mean(np.asarray(res), axis=0)\n","res40"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 13.872467\n","[SoftImpute] Iter 1: observed MAE=0.022019 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022079 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022138 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022189 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022236 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022277 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022315 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022351 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022385 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022417 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022447 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022476 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022501 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022523 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022544 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022561 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022577 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022590 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.022601 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.022611 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.022619 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.022626 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.022632 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.022638 rank=13\n","[SoftImpute] Iter 25: observed MAE=0.022644 rank=13\n","[SoftImpute] Iter 26: observed MAE=0.022650 rank=13\n","[SoftImpute] Iter 27: observed MAE=0.022655 rank=13\n","[SoftImpute] Iter 28: observed MAE=0.022659 rank=13\n","[SoftImpute] Iter 29: observed MAE=0.022663 rank=13\n","[SoftImpute] Iter 30: observed MAE=0.022667 rank=13\n","[SoftImpute] Iter 31: observed MAE=0.022671 rank=13\n","[SoftImpute] Iter 32: observed MAE=0.022676 rank=13\n","[SoftImpute] Iter 33: observed MAE=0.022680 rank=13\n","[SoftImpute] Iter 34: observed MAE=0.022684 rank=13\n","[SoftImpute] Iter 35: observed MAE=0.022687 rank=13\n","[SoftImpute] Iter 36: observed MAE=0.022691 rank=13\n","[SoftImpute] Iter 37: observed MAE=0.022695 rank=13\n","[SoftImpute] Iter 38: observed MAE=0.022699 rank=13\n","[SoftImpute] Iter 39: observed MAE=0.022703 rank=13\n","[SoftImpute] Iter 40: observed MAE=0.022706 rank=13\n","[SoftImpute] Iter 41: observed MAE=0.022710 rank=13\n","[SoftImpute] Iter 42: observed MAE=0.022713 rank=13\n","[SoftImpute] Iter 43: observed MAE=0.022716 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.022719 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.022723 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.022726 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.022729 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.022732 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.022736 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.022739 rank=13\n","[SoftImpute] Iter 51: observed MAE=0.022742 rank=13\n","[SoftImpute] Iter 52: observed MAE=0.022744 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.022747 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.022750 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.022752 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.022755 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.022757 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.022759 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.022761 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.022763 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.022765 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.022767 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.022769 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.022771 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.022773 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.022775 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.022777 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.022778 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.022780 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022781 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022783 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022784 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022786 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022787 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022788 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022790 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022791 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022792 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022794 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022795 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022796 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022798 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022799 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022800 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022802 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022803 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022804 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022805 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022806 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022807 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022808 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022810 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022811 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.022812 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.022813 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.022814 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.022815 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.022816 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.022817 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.022818 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.277449\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22648\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15064, constraints m = 18652\n","Cones:\tprimal zero / dual free vars: 1794\n","\tlinear vars: 5382\n","\tsd vars: 11476, sd blks: 1\n","Setup time: 2.22e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.52e+21  1.43e+21  1.00e+00 -1.62e+23  3.29e+22  4.99e+22  1.57e-02 \n","   100| 2.26e-03  3.44e-03  2.61e-04  3.67e+01  3.67e+01  2.47e-14  1.74e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.74e+00s\n","\tLin-sys: nnz in L factor: 57465, avg solve time: 4.22e-04s\n","\tCones: avg projection time: 1.18e-02s\n","\tAcceleration: avg step time: 4.09e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.8588e-09, dist(y, K*) = 1.7956e-09, s'y/|s||y| = -1.0942e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.9274e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.4397e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.5715e-05\n","----------------------------------------------------------------------------\n","c'x = 36.6396, -b'y = 36.6415\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.256940\n","[SoftImpute] Iter 1: observed MAE=0.022840 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022875 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022902 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022924 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022944 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022963 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022980 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022999 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.023017 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.023038 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.023059 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.023079 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.023099 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.023121 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.023141 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.023159 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.023174 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.023188 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.023202 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.023214 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.023225 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.023235 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.023245 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.023254 rank=13\n","[SoftImpute] Iter 25: observed MAE=0.023262 rank=13\n","[SoftImpute] Iter 26: observed MAE=0.023269 rank=13\n","[SoftImpute] Iter 27: observed MAE=0.023276 rank=13\n","[SoftImpute] Iter 28: observed MAE=0.023282 rank=13\n","[SoftImpute] Iter 29: observed MAE=0.023289 rank=13\n","[SoftImpute] Iter 30: observed MAE=0.023294 rank=13\n","[SoftImpute] Iter 31: observed MAE=0.023299 rank=13\n","[SoftImpute] Iter 32: observed MAE=0.023303 rank=13\n","[SoftImpute] Iter 33: observed MAE=0.023307 rank=13\n","[SoftImpute] Iter 34: observed MAE=0.023311 rank=13\n","[SoftImpute] Iter 35: observed MAE=0.023315 rank=13\n","[SoftImpute] Iter 36: observed MAE=0.023319 rank=13\n","[SoftImpute] Iter 37: observed MAE=0.023322 rank=13\n","[SoftImpute] Iter 38: observed MAE=0.023325 rank=13\n","[SoftImpute] Iter 39: observed MAE=0.023328 rank=13\n","[SoftImpute] Iter 40: observed MAE=0.023331 rank=13\n","[SoftImpute] Iter 41: observed MAE=0.023334 rank=13\n","[SoftImpute] Iter 42: observed MAE=0.023338 rank=13\n","[SoftImpute] Iter 43: observed MAE=0.023341 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.023344 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.023346 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.023349 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.023352 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.023354 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.023356 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.023359 rank=13\n","[SoftImpute] Iter 51: observed MAE=0.023361 rank=13\n","[SoftImpute] Iter 52: observed MAE=0.023363 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.023365 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.023367 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.023370 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.023372 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.023374 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.023376 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.023378 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.023380 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.023382 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.023384 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.023386 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.023387 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.023389 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.023391 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.023392 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.023394 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.023395 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.023397 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.023398 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.023400 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.023401 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.023403 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.023404 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.023405 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.023407 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.023408 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.023409 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.023411 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.023412 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.023413 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.023414 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.023415 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.023416 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.023417 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.023419 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.023420 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.023421 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.023422 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.023422 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.023423 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.023424 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.023425 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.023426 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.023427 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.023428 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.023428 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.023429 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.023430 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.285139\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22648\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15064, constraints m = 18652\n","Cones:\tprimal zero / dual free vars: 1794\n","\tlinear vars: 5382\n","\tsd vars: 11476, sd blks: 1\n","Setup time: 2.11e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.52e+21  1.43e+21  1.00e+00 -1.65e+23  3.36e+22  5.09e+22  1.71e-02 \n","   100| 1.52e+00  4.72e-01  9.47e-01  3.77e+01  5.46e-01  8.52e-15  1.74e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.74e+00s\n","\tLin-sys: nnz in L factor: 57465, avg solve time: 4.21e-04s\n","\tCones: avg projection time: 1.18e-02s\n","\tAcceleration: avg step time: 4.04e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6265e-09, dist(y, K*) = 1.1429e-08, s'y/|s||y| = -6.1026e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.8553e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.4934e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 4.1071e-05\n","----------------------------------------------------------------------------\n","c'x = 37.6153, -b'y = 37.6184\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.939775\n","[SoftImpute] Iter 1: observed MAE=0.022083 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022134 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022175 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022209 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022240 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022268 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022296 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022321 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022343 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022363 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022381 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022399 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022416 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022430 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022442 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022451 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022459 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022465 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.022470 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.022474 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.022479 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.022484 rank=13\n","[SoftImpute] Iter 23: observed 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Iter 59: observed MAE=0.022584 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.022586 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.022587 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.022589 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.022590 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.022592 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.022593 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.022595 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.022596 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.022598 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.022599 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022601 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022602 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022603 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022605 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022606 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022607 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022608 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022609 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022610 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022611 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022612 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022613 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022614 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022615 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022616 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022617 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022618 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022619 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022619 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022620 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022621 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022622 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022622 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022623 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.022624 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.022625 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.022625 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.022626 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.022627 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.022627 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.022628 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.278796\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 24673\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 16702, constraints m = 20524\n","Cones:\tprimal zero / dual free vars: 1911\n","\tlinear vars: 5733\n","\tsd vars: 12880, sd blks: 1\n","Setup time: 3.19e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.61e+21  1.52e+21  1.00e+00 -1.78e+23  3.59e+22  5.35e+22  1.60e-02 \n","   100| 1.37e-03  1.77e-03  1.57e-04  3.68e+01  3.68e+01  1.07e-14  1.83e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.83e+00s\n","\tLin-sys: nnz in L factor: 63018, avg solve time: 4.61e-04s\n","\tCones: avg projection time: 1.22e-02s\n","\tAcceleration: avg step time: 4.53e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6732e-09, dist(y, K*) = 8.6455e-10, s'y/|s||y| = 2.0548e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.9245e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.2611e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.6716e-05\n","----------------------------------------------------------------------------\n","c'x = 36.7414, -b'y = 36.7387\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.959774\n","[SoftImpute] Iter 1: observed MAE=0.021943 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022007 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022062 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022108 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022146 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022178 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022205 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022228 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022247 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022263 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022276 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022287 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022298 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022310 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022322 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022332 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022340 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022346 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.022351 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.022356 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.022359 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.022362 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.022364 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.022366 rank=13\n","[SoftImpute] Iter 25: observed MAE=0.022368 rank=13\n","[SoftImpute] Iter 26: observed MAE=0.022370 rank=13\n","[SoftImpute] Iter 27: observed MAE=0.022372 rank=13\n","[SoftImpute] Iter 28: observed 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observed MAE=0.022404 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.022406 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.022409 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.022411 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.022413 rank=13\n","[SoftImpute] Iter 51: observed MAE=0.022415 rank=13\n","[SoftImpute] Iter 52: observed MAE=0.022417 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.022419 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.022420 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.022422 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.022424 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.022426 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.022427 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.022429 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.022431 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.022432 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.022434 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.022436 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.022437 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.022439 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.022441 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.022442 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.022444 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.022445 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022446 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022448 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022449 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022450 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022452 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022453 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022454 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022455 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022457 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022458 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022459 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022460 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022461 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022462 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022463 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022464 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022465 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022465 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022466 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022467 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022468 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022469 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022470 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022470 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.022471 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.022472 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.022472 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.022473 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.022474 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.022474 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.022475 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.279195\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 25366\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17266, constraints m = 21166\n","Cones:\tprimal zero / dual free vars: 1950\n","\tlinear vars: 5850\n","\tsd vars: 13366, sd blks: 1\n","Setup time: 2.76e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.64e+21  1.55e+21  1.00e+00 -1.84e+23  3.70e+22  5.49e+22  1.78e-02 \n","   100| 1.78e-03  2.67e-03  7.56e-05  3.71e+01  3.71e+01  5.27e-15  1.96e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.96e+00s\n","\tLin-sys: nnz in L factor: 64923, avg solve time: 4.69e-04s\n","\tCones: avg projection time: 1.31e-02s\n","\tAcceleration: avg step time: 4.86e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6759e-09, dist(y, K*) = 1.8470e-09, s'y/|s||y| = 6.0215e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.1191e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.6889e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.4484e-04\n","----------------------------------------------------------------------------\n","c'x = 37.1192, -b'y = 37.0932\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.662203\n","[SoftImpute] Iter 1: observed MAE=0.021565 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.021612 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.021653 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.021687 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.021717 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.021746 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.021773 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.021796 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.021818 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.021839 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.021859 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.021877 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.021893 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.021908 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.021922 rank=13\n","[SoftImpute] Iter 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rank=13\n","[SoftImpute] Iter 34: observed MAE=0.022083 rank=13\n","[SoftImpute] Iter 35: observed MAE=0.022088 rank=13\n","[SoftImpute] Iter 36: observed MAE=0.022092 rank=13\n","[SoftImpute] Iter 37: observed MAE=0.022095 rank=13\n","[SoftImpute] Iter 38: observed MAE=0.022099 rank=13\n","[SoftImpute] Iter 39: observed MAE=0.022102 rank=13\n","[SoftImpute] Iter 40: observed MAE=0.022105 rank=13\n","[SoftImpute] Iter 41: observed MAE=0.022108 rank=13\n","[SoftImpute] Iter 42: observed MAE=0.022111 rank=13\n","[SoftImpute] Iter 43: observed MAE=0.022114 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.022117 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.022120 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.022123 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.022125 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.022128 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.022130 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.022132 rank=13\n","[SoftImpute] Iter 51: observed 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observed MAE=0.022164 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022165 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022166 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022168 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022169 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022170 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022171 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022172 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022173 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022174 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022175 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022176 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022177 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022178 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022179 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022180 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022180 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022181 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022182 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022183 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022184 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022184 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022185 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022186 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022187 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.022187 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.022188 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.022188 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.022189 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.022190 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.022190 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.022191 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.273244\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22869\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15242, constraints m = 18856\n","Cones:\tprimal zero / dual free vars: 1807\n","\tlinear vars: 5421\n","\tsd vars: 11628, sd blks: 1\n","Setup time: 2.30e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.53e+21  1.44e+21  1.00e+00 -1.62e+23  3.29e+22  4.97e+22  1.90e-02 \n","   100| 2.13e-03  2.81e-03  1.64e-05  3.71e+01  3.71e+01  2.57e-15  1.76e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.76e+00s\n","\tLin-sys: nnz in L factor: 58070, avg solve time: 4.25e-04s\n","\tCones: avg projection time: 1.19e-02s\n","\tAcceleration: avg step time: 4.21e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7471e-09, dist(y, K*) = 1.6017e-09, s'y/|s||y| = 6.8075e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.6882e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.5316e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.9939e-04\n","----------------------------------------------------------------------------\n","c'x = 37.0937, -b'y = 37.0787\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.01145161, 0.05099374, 0.01657982, 0.02859447, 0.11274784,\n","       0.02859447, 0.39993818])"]},"metadata":{"tags":[]},"execution_count":19}]},{"cell_type":"markdown","metadata":{"id":"AfDtDQqO9CbL"},"source":["##50%"]},{"cell_type":"code","metadata":{"id":"Ga8Cukg59E9o","executionInfo":{"status":"ok","timestamp":1604556370014,"user_tz":360,"elapsed":17572,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"5ec2d1fa-a9f6-4887-f38a-d67236627a11","colab":{"base_uri":"https://localhost:8080/"}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),30,24,22], [sum(ytrain==1),35,30,26],\n","                  [sum(ytrain==2),26,25,22]])\n","    p = np.array([2,4,5,13])  \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res50 = np.mean(np.asarray(res), axis=0)\n","res50"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 13.928192\n","[SoftImpute] Iter 1: observed MAE=0.022406 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022464 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022511 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022549 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022579 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022604 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022625 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022642 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022657 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022671 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022683 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022694 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022705 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022715 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022725 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022733 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022741 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022748 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.022754 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.022760 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.022765 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.022770 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.022774 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.022778 rank=13\n","[SoftImpute] Iter 25: observed MAE=0.022782 rank=13\n","[SoftImpute] Iter 26: observed MAE=0.022786 rank=13\n","[SoftImpute] Iter 27: observed MAE=0.022790 rank=13\n","[SoftImpute] Iter 28: observed MAE=0.022794 rank=13\n","[SoftImpute] Iter 29: observed MAE=0.022798 rank=13\n","[SoftImpute] Iter 30: observed MAE=0.022802 rank=13\n","[SoftImpute] Iter 31: observed MAE=0.022806 rank=13\n","[SoftImpute] Iter 32: observed MAE=0.022810 rank=13\n","[SoftImpute] Iter 33: observed MAE=0.022813 rank=13\n","[SoftImpute] Iter 34: observed MAE=0.022816 rank=13\n","[SoftImpute] Iter 35: observed MAE=0.022819 rank=13\n","[SoftImpute] Iter 36: observed MAE=0.022822 rank=13\n","[SoftImpute] Iter 37: observed MAE=0.022825 rank=13\n","[SoftImpute] Iter 38: observed MAE=0.022828 rank=13\n","[SoftImpute] Iter 39: observed MAE=0.022831 rank=13\n","[SoftImpute] Iter 40: observed MAE=0.022834 rank=13\n","[SoftImpute] Iter 41: observed MAE=0.022837 rank=13\n","[SoftImpute] Iter 42: observed MAE=0.022840 rank=13\n","[SoftImpute] Iter 43: observed MAE=0.022843 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.022846 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.022850 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.022853 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.022856 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.022858 rank=13\n","[SoftImpute] Iter 49: observed 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observed MAE=0.022901 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.022903 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.022905 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022907 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022909 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022911 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022913 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022915 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022917 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022919 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022920 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022922 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022924 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022925 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022927 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022928 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022930 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022931 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022932 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022934 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022935 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022936 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022937 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022938 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022940 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022941 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022942 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.022943 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.022944 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.022945 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.022946 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.022947 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.022948 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.022949 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.278564\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22640\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15064, constraints m = 18652\n","Cones:\tprimal zero / dual free vars: 1794\n","\tlinear vars: 5382\n","\tsd vars: 11476, sd blks: 1\n","Setup time: 2.09e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.52e+21  1.43e+21  1.00e+00 -1.62e+23  3.29e+22  4.98e+22  1.92e-02 \n","   100| 7.67e-04  1.20e-03  3.68e-06  3.66e+01  3.66e+01  2.93e-15  1.76e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.76e+00s\n","\tLin-sys: nnz in L factor: 57453, avg solve time: 4.30e-04s\n","\tCones: avg projection time: 1.17e-02s\n","\tAcceleration: avg step time: 4.35e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7468e-09, dist(y, K*) = 2.0685e-09, s'y/|s||y| = 3.7894e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.0033e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.0856e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.8149e-04\n","----------------------------------------------------------------------------\n","c'x = 36.6124, -b'y = 36.5989\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.465772\n","[SoftImpute] Iter 1: observed MAE=0.023604 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.023646 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.023679 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.023707 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.023730 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.023748 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.023762 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.023775 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.023787 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.023796 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.023804 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.023811 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.023817 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.023823 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.023829 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.023835 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.023841 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.023846 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.023851 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.023855 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.023859 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.023862 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.023866 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.023869 rank=13\n","[SoftImpute] Iter 25: observed MAE=0.023873 rank=13\n","[SoftImpute] Iter 26: observed MAE=0.023876 rank=13\n","[SoftImpute] Iter 27: observed MAE=0.023879 rank=13\n","[SoftImpute] Iter 28: observed MAE=0.023882 rank=13\n","[SoftImpute] Iter 29: observed MAE=0.023885 rank=13\n","[SoftImpute] Iter 30: observed MAE=0.023887 rank=13\n","[SoftImpute] Iter 31: observed MAE=0.023890 rank=13\n","[SoftImpute] Iter 32: observed MAE=0.023893 rank=13\n","[SoftImpute] Iter 33: observed MAE=0.023896 rank=13\n","[SoftImpute] Iter 34: observed MAE=0.023899 rank=13\n","[SoftImpute] Iter 35: observed MAE=0.023902 rank=13\n","[SoftImpute] Iter 36: observed MAE=0.023905 rank=13\n","[SoftImpute] Iter 37: observed MAE=0.023908 rank=13\n","[SoftImpute] Iter 38: observed MAE=0.023911 rank=13\n","[SoftImpute] Iter 39: observed MAE=0.023914 rank=13\n","[SoftImpute] Iter 40: observed MAE=0.023918 rank=13\n","[SoftImpute] Iter 41: observed MAE=0.023921 rank=13\n","[SoftImpute] Iter 42: observed MAE=0.023925 rank=13\n","[SoftImpute] Iter 43: observed MAE=0.023928 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.023931 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.023934 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.023937 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.023939 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.023942 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.023945 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.023947 rank=13\n","[SoftImpute] Iter 51: observed MAE=0.023950 rank=13\n","[SoftImpute] Iter 52: observed MAE=0.023952 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.023955 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.023957 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.023959 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.023962 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.023964 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.023967 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.023969 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.023971 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.023973 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.023975 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.023977 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.023979 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.023981 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.023984 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.023986 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.023988 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.023990 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.023991 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.023993 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.023995 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.023997 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.023998 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.024000 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.024001 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.024003 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.024004 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.024006 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.024007 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.024009 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.024010 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.024011 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.024013 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.024014 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.024015 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.024016 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.024017 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.024018 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.024020 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.024021 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.024022 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.024023 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.024024 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.024024 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.024025 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.024026 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.024027 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.024028 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.024029 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.289315\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22640\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15064, constraints m = 18652\n","Cones:\tprimal zero / dual free vars: 1794\n","\tlinear vars: 5382\n","\tsd vars: 11476, sd blks: 1\n","Setup time: 2.19e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.52e+21  1.43e+21  1.00e+00 -1.66e+23  3.38e+22  5.12e+22  1.92e-02 \n","   100| 1.52e-03  2.32e-03  2.84e-04  3.77e+01  3.77e+01  1.76e-14  1.82e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.82e+00s\n","\tLin-sys: nnz in L factor: 57453, avg solve time: 4.47e-04s\n","\tCones: avg projection time: 1.21e-02s\n","\tAcceleration: avg step time: 4.56e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7507e-09, dist(y, K*) = 1.7121e-09, s'y/|s||y| = 1.2472e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.0627e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.5514e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 4.9777e-06\n","----------------------------------------------------------------------------\n","c'x = 37.7140, -b'y = 37.7144\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.997877\n","[SoftImpute] Iter 1: observed MAE=0.022273 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022330 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022373 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022407 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022435 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022458 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022476 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022492 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022505 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022516 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022526 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022537 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022546 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022555 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022563 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022572 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022579 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022586 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.022592 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.022598 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.022603 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.022608 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.022612 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.022616 rank=13\n","[SoftImpute] Iter 25: observed MAE=0.022620 rank=13\n","[SoftImpute] Iter 26: observed MAE=0.022624 rank=13\n","[SoftImpute] Iter 27: observed MAE=0.022627 rank=13\n","[SoftImpute] Iter 28: observed MAE=0.022630 rank=13\n","[SoftImpute] Iter 29: observed MAE=0.022633 rank=13\n","[SoftImpute] Iter 30: observed MAE=0.022636 rank=13\n","[SoftImpute] Iter 31: observed MAE=0.022639 rank=13\n","[SoftImpute] Iter 32: observed MAE=0.022642 rank=13\n","[SoftImpute] Iter 33: observed MAE=0.022644 rank=13\n","[SoftImpute] Iter 34: observed MAE=0.022646 rank=13\n","[SoftImpute] Iter 35: observed MAE=0.022649 rank=13\n","[SoftImpute] Iter 36: observed MAE=0.022651 rank=13\n","[SoftImpute] Iter 37: observed MAE=0.022652 rank=13\n","[SoftImpute] Iter 38: observed MAE=0.022654 rank=13\n","[SoftImpute] Iter 39: observed MAE=0.022655 rank=13\n","[SoftImpute] Iter 40: observed MAE=0.022657 rank=13\n","[SoftImpute] Iter 41: observed MAE=0.022658 rank=13\n","[SoftImpute] Iter 42: observed MAE=0.022659 rank=13\n","[SoftImpute] Iter 43: observed MAE=0.022660 rank=13\n","[SoftImpute] Iter 44: observed MAE=0.022661 rank=13\n","[SoftImpute] Iter 45: observed MAE=0.022663 rank=13\n","[SoftImpute] Iter 46: observed MAE=0.022664 rank=13\n","[SoftImpute] Iter 47: observed MAE=0.022665 rank=13\n","[SoftImpute] Iter 48: observed MAE=0.022667 rank=13\n","[SoftImpute] Iter 49: observed MAE=0.022668 rank=13\n","[SoftImpute] Iter 50: observed MAE=0.022670 rank=13\n","[SoftImpute] Iter 51: observed MAE=0.022671 rank=13\n","[SoftImpute] Iter 52: observed MAE=0.022673 rank=13\n","[SoftImpute] Iter 53: observed MAE=0.022674 rank=13\n","[SoftImpute] Iter 54: observed MAE=0.022675 rank=13\n","[SoftImpute] Iter 55: observed MAE=0.022677 rank=13\n","[SoftImpute] Iter 56: observed MAE=0.022679 rank=13\n","[SoftImpute] Iter 57: observed MAE=0.022680 rank=13\n","[SoftImpute] Iter 58: observed MAE=0.022682 rank=13\n","[SoftImpute] Iter 59: observed MAE=0.022683 rank=13\n","[SoftImpute] Iter 60: observed MAE=0.022684 rank=13\n","[SoftImpute] Iter 61: observed MAE=0.022686 rank=13\n","[SoftImpute] Iter 62: observed MAE=0.022687 rank=13\n","[SoftImpute] Iter 63: observed MAE=0.022688 rank=13\n","[SoftImpute] Iter 64: observed MAE=0.022689 rank=13\n","[SoftImpute] Iter 65: observed MAE=0.022691 rank=13\n","[SoftImpute] Iter 66: observed MAE=0.022692 rank=13\n","[SoftImpute] Iter 67: observed MAE=0.022693 rank=13\n","[SoftImpute] Iter 68: observed MAE=0.022694 rank=13\n","[SoftImpute] Iter 69: observed MAE=0.022695 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022696 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022697 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022698 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022699 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022700 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022701 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022702 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022703 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022705 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022706 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022707 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022708 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022708 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022709 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022710 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022711 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022712 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022713 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022714 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022715 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022715 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022716 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022717 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022718 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.022718 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.022719 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.022720 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.022721 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.022721 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.022722 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.022722 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.279958\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 24665\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 16702, constraints m = 20524\n","Cones:\tprimal zero / dual free vars: 1911\n","\tlinear vars: 5733\n","\tsd vars: 12880, sd blks: 1\n","Setup time: 2.25e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.61e+21  1.52e+21  1.00e+00 -1.78e+23  3.58e+22  5.34e+22  1.85e-02 \n","   100| 6.06e-03  9.80e-03  7.17e-04  3.69e+01  3.69e+01  2.86e-15  1.87e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.87e+00s\n","\tLin-sys: nnz in L factor: 63006, avg solve time: 4.66e-04s\n","\tCones: avg projection time: 1.22e-02s\n","\tAcceleration: avg step time: 4.84e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7985e-09, dist(y, K*) = 1.2835e-09, s'y/|s||y| = -7.5661e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.3151e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.2972e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.7621e-04\n","----------------------------------------------------------------------------\n","c'x = 36.8647, -b'y = 36.8515\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 14.025763\n","[SoftImpute] Iter 1: observed MAE=0.022053 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.022115 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.022167 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.022208 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.022242 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022270 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022294 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022314 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022331 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022347 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022361 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022373 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022384 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022393 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022402 rank=13\n","[SoftImpute] Iter 16: observed MAE=0.022410 rank=13\n","[SoftImpute] Iter 17: observed MAE=0.022418 rank=13\n","[SoftImpute] Iter 18: observed MAE=0.022424 rank=13\n","[SoftImpute] Iter 19: observed MAE=0.022431 rank=13\n","[SoftImpute] Iter 20: observed MAE=0.022437 rank=13\n","[SoftImpute] Iter 21: observed MAE=0.022443 rank=13\n","[SoftImpute] Iter 22: observed MAE=0.022449 rank=13\n","[SoftImpute] Iter 23: observed MAE=0.022455 rank=13\n","[SoftImpute] Iter 24: observed MAE=0.022460 rank=13\n","[SoftImpute] Iter 25: observed MAE=0.022464 rank=13\n","[SoftImpute] Iter 26: observed MAE=0.022469 rank=13\n","[SoftImpute] Iter 27: observed MAE=0.022473 rank=13\n","[SoftImpute] Iter 28: observed 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rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022592 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022593 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022594 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022595 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022596 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022597 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022598 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022599 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022600 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022600 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022601 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022602 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.022603 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.022604 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.022604 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.022605 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.022606 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.022606 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.022607 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.280515\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 25358\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 17266, constraints m = 21166\n","Cones:\tprimal zero / dual free vars: 1950\n","\tlinear vars: 5850\n","\tsd vars: 13366, sd blks: 1\n","Setup time: 2.54e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.64e+21  1.55e+21  1.00e+00 -1.84e+23  3.70e+22  5.49e+22  2.16e-02 \n","   100| 6.89e-03  1.02e-02  3.48e-04  3.72e+01  3.73e+01  8.42e-15  2.01e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 2.01e+00s\n","\tLin-sys: nnz in L factor: 64911, avg solve time: 4.77e-04s\n","\tCones: avg projection time: 1.33e-02s\n","\tAcceleration: avg step time: 5.07e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.5922e-09, dist(y, K*) = 3.9113e-09, s'y/|s||y| = 4.6337e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.0330e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.2406e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.1503e-04\n","----------------------------------------------------------------------------\n","c'x = 37.2378, -b'y = 37.2216\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 13.711229\n","[SoftImpute] Iter 1: observed MAE=0.021819 rank=13\n","[SoftImpute] Iter 2: observed MAE=0.021878 rank=13\n","[SoftImpute] Iter 3: observed MAE=0.021925 rank=13\n","[SoftImpute] Iter 4: observed MAE=0.021964 rank=13\n","[SoftImpute] Iter 5: observed MAE=0.021995 rank=13\n","[SoftImpute] Iter 6: observed MAE=0.022021 rank=13\n","[SoftImpute] Iter 7: observed MAE=0.022043 rank=13\n","[SoftImpute] Iter 8: observed MAE=0.022062 rank=13\n","[SoftImpute] Iter 9: observed MAE=0.022079 rank=13\n","[SoftImpute] Iter 10: observed MAE=0.022096 rank=13\n","[SoftImpute] Iter 11: observed MAE=0.022111 rank=13\n","[SoftImpute] Iter 12: observed MAE=0.022124 rank=13\n","[SoftImpute] Iter 13: observed MAE=0.022135 rank=13\n","[SoftImpute] Iter 14: observed MAE=0.022146 rank=13\n","[SoftImpute] Iter 15: observed MAE=0.022157 rank=13\n","[SoftImpute] Iter 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observed MAE=0.022353 rank=13\n","[SoftImpute] Iter 70: observed MAE=0.022354 rank=13\n","[SoftImpute] Iter 71: observed MAE=0.022355 rank=13\n","[SoftImpute] Iter 72: observed MAE=0.022357 rank=13\n","[SoftImpute] Iter 73: observed MAE=0.022358 rank=13\n","[SoftImpute] Iter 74: observed MAE=0.022359 rank=13\n","[SoftImpute] Iter 75: observed MAE=0.022360 rank=13\n","[SoftImpute] Iter 76: observed MAE=0.022361 rank=13\n","[SoftImpute] Iter 77: observed MAE=0.022362 rank=13\n","[SoftImpute] Iter 78: observed MAE=0.022363 rank=13\n","[SoftImpute] Iter 79: observed MAE=0.022364 rank=13\n","[SoftImpute] Iter 80: observed MAE=0.022365 rank=13\n","[SoftImpute] Iter 81: observed MAE=0.022366 rank=13\n","[SoftImpute] Iter 82: observed MAE=0.022367 rank=13\n","[SoftImpute] Iter 83: observed MAE=0.022368 rank=13\n","[SoftImpute] Iter 84: observed MAE=0.022369 rank=13\n","[SoftImpute] Iter 85: observed MAE=0.022370 rank=13\n","[SoftImpute] Iter 86: observed MAE=0.022370 rank=13\n","[SoftImpute] Iter 87: observed MAE=0.022371 rank=13\n","[SoftImpute] Iter 88: observed MAE=0.022372 rank=13\n","[SoftImpute] Iter 89: observed MAE=0.022373 rank=13\n","[SoftImpute] Iter 90: observed MAE=0.022374 rank=13\n","[SoftImpute] Iter 91: observed MAE=0.022374 rank=13\n","[SoftImpute] Iter 92: observed MAE=0.022375 rank=13\n","[SoftImpute] Iter 93: observed MAE=0.022376 rank=13\n","[SoftImpute] Iter 94: observed MAE=0.022376 rank=13\n","[SoftImpute] Iter 95: observed MAE=0.022377 rank=13\n","[SoftImpute] Iter 96: observed MAE=0.022378 rank=13\n","[SoftImpute] Iter 97: observed MAE=0.022378 rank=13\n","[SoftImpute] Iter 98: observed MAE=0.022379 rank=13\n","[SoftImpute] Iter 99: observed MAE=0.022379 rank=13\n","[SoftImpute] Iter 100: observed MAE=0.022380 rank=13\n","[SoftImpute] Stopped after iteration 100 for lambda=0.274225\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 22861\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 15242, constraints m = 18856\n","Cones:\tprimal zero / dual free vars: 1807\n","\tlinear vars: 5421\n","\tsd vars: 11628, sd blks: 1\n","Setup time: 2.12e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.53e+21  1.44e+21  1.00e+00 -1.62e+23  3.28e+22  4.96e+22  1.78e-02 \n","   100| 4.19e-03  6.38e-03  3.11e-04  3.70e+01  3.69e+01  8.02e-15  1.78e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.78e+00s\n","\tLin-sys: nnz in L factor: 58058, avg solve time: 4.30e-04s\n","\tCones: avg projection time: 1.18e-02s\n","\tAcceleration: avg step time: 4.48e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.8221e-09, dist(y, K*) = 1.5593e-09, s'y/|s||y| = 7.4512e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.4222e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.6334e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.4636e-05\n","----------------------------------------------------------------------------\n","c'x = 36.9578, -b'y = 36.9567\n","============================================================================\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["array([0.01145161, 0.05599374, 0.01657982, 0.03359447, 0.06958821,\n","       0.03359447, 0.40210165])"]},"metadata":{"tags":[]},"execution_count":47}]},{"cell_type":"code","metadata":{"id":"rgXhpxsr9utb"},"source":[""],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"0S8i0kZ97gPY"},"source":["## results"]},{"cell_type":"code","metadata":{"id":"32B-CF_GMP8i","executionInfo":{"status":"ok","timestamp":1591370902058,"user_tz":300,"elapsed":151289,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"837a999f-b9b0-4b34-a316-837b6b55fab4","colab":{"base_uri":"https://localhost:8080/","height":118}},"source":["wine = np.vstack((res20, res30, res40))\n","wine"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[0.01145161, 0.02504608, 0.01790323, 0.01290323, 0.03004608,\n","        0.01290323, 0.20108013],\n","       [0.01145161, 0.0414977 , 0.01790323, 0.01645161, 0.05175411,\n","        0.01645161, 0.30420463],\n","       [0.01145161, 0.05099374, 0.01657982, 0.02859447, 0.11274784,\n","        0.02859447, 0.39993818]])"]},"metadata":{"tags":[]},"execution_count":20}]},{"cell_type":"markdown","metadata":{"id":"JE_FulEEAamU"},"source":["# Iris\n","The data set is also available in sklearn, as noted in the package's website. So, we load it directly from sklearn"]},{"cell_type":"code","metadata":{"id":"j_I06dv4Be8l"},"source":["iris = datasets.load_iris()\n","X,y = iris.data, iris.target.ravel() "],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"EeD_xY-jAc6h","executionInfo":{"status":"ok","timestamp":1604556534667,"user_tz":360,"elapsed":8953,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"acc6f3d5-da4f-415d-f6b8-feb3543ce498","colab":{"base_uri":"https://localhost:8080/"}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),30,28], [sum(ytrain==1),30,27],\n","                  [sum(ytrain==2),30,27]])\n","    p = np.array([1,3,4])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res20 = np.mean(np.asarray(res), axis=0)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 9.360055\n","[SoftImpute] Iter 1: observed MAE=0.013556 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013579 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013607 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013639 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013688 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013742 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013803 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013869 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013940 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.014010 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.014079 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.014144 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.014205 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.014266 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.014323 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.014373 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.014416 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.014452 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.014483 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.014511 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.014537 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.014559 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.014580 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.014598 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.014615 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.014632 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.014646 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.014660 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.014673 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.014686 rank=4\n","[SoftImpute] Iter 31: observed 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lambda=0.187201\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 10623\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 8447, constraints m = 9391\n","Cones:\tprimal zero / dual free vars: 472\n","\tlinear vars: 1416\n","\tsd vars: 7503, sd blks: 1\n","Setup time: 1.84e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.16e+21  1.07e+21  1.00e+00 -7.22e+22  1.33e+22  1.82e+22  1.39e-02 \n","   100| 3.50e-04  3.43e-04  1.06e-04  1.48e+01  1.48e+01  1.12e-15  1.06e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.06e+00s\n","\tLin-sys: nnz in L factor: 28841, avg solve time: 2.23e-04s\n","\tCones: avg projection time: 7.58e-03s\n","\tAcceleration: avg step time: 2.21e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3606e-09, dist(y, K*) = 2.0470e-09, s'y/|s||y| = -1.1693e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.4964e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.4307e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.0630e-04\n","----------------------------------------------------------------------------\n","c'x = 14.7596, -b'y = 14.7628\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 9.194000\n","[SoftImpute] Iter 1: observed MAE=0.013508 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013520 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013534 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013562 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013598 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013636 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013675 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013723 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013777 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013844 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013911 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013977 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.014039 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.014093 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.014141 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.014184 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.014222 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.014254 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.014281 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.014305 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.014324 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.014341 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.014356 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.014370 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.014382 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.014394 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.014405 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.014416 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.014425 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.014435 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.014444 rank=4\n","[SoftImpute] Iter 32: observed MAE=0.014453 rank=4\n","[SoftImpute] Iter 33: observed MAE=0.014462 rank=4\n","[SoftImpute] Iter 34: observed MAE=0.014471 rank=4\n","[SoftImpute] Iter 35: observed MAE=0.014480 rank=4\n","[SoftImpute] Iter 36: observed MAE=0.014488 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rank=4\n","[SoftImpute] Iter 55: observed MAE=0.014592 rank=4\n","[SoftImpute] Iter 56: observed MAE=0.014595 rank=4\n","[SoftImpute] Iter 57: observed MAE=0.014598 rank=4\n","[SoftImpute] Iter 58: observed MAE=0.014601 rank=4\n","[SoftImpute] Iter 59: observed MAE=0.014604 rank=4\n","[SoftImpute] Iter 60: observed MAE=0.014606 rank=4\n","[SoftImpute] Iter 61: observed MAE=0.014609 rank=4\n","[SoftImpute] Iter 62: observed MAE=0.014611 rank=4\n","[SoftImpute] Iter 63: observed MAE=0.014613 rank=4\n","[SoftImpute] Iter 64: observed MAE=0.014615 rank=4\n","[SoftImpute] Iter 65: observed MAE=0.014617 rank=4\n","[SoftImpute] Iter 66: observed MAE=0.014619 rank=4\n","[SoftImpute] Iter 67: observed MAE=0.014620 rank=4\n","[SoftImpute] Iter 68: observed MAE=0.014622 rank=4\n","[SoftImpute] Iter 69: observed MAE=0.014624 rank=4\n","[SoftImpute] Iter 70: observed MAE=0.014625 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.014626 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.014628 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.014629 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.014630 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.014631 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.014632 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.014633 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.014634 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.014634 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.014635 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.014636 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.014637 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.014637 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.014638 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.014639 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.014639 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.014640 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.014640 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.014641 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.014641 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.014642 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.014642 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.014642 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.014643 rank=4\n","[SoftImpute] Stopped after iteration 94 for lambda=0.183880\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 9913\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 7807, constraints m = 8711\n","Cones:\tprimal zero / dual free vars: 452\n","\tlinear vars: 1356\n","\tsd vars: 6903, sd blks: 1\n","Setup time: 1.26e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.11e+21  1.02e+21  1.00e+00 -6.66e+22  1.23e+22  1.71e+22  8.34e-03 \n","   100| 1.06e-03  1.07e-03  1.12e-04  1.45e+01  1.45e+01  2.17e-15  9.42e-01 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 9.42e-01s\n","\tLin-sys: nnz in L factor: 26806, avg solve time: 1.95e-04s\n","\tCones: avg projection time: 6.58e-03s\n","\tAcceleration: avg step time: 2.08e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.4105e-09, dist(y, K*) = 1.5770e-09, s'y/|s||y| = 6.9430e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.7498e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.4161e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.8675e-04\n","----------------------------------------------------------------------------\n","c'x = 14.5065, -b'y = 14.5009\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 9.305317\n","[SoftImpute] Iter 1: observed MAE=0.013359 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013382 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013410 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013440 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013474 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013514 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013554 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013594 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013638 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013691 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013742 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013791 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013841 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013887 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013929 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.013966 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.014000 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.014029 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.014054 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.014076 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.014095 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.014112 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.014128 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.014142 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.014155 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.014167 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.014179 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.014190 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.014201 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.014212 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.014222 rank=4\n","[SoftImpute] Iter 32: observed MAE=0.014232 rank=4\n","[SoftImpute] Iter 33: observed MAE=0.014242 rank=4\n","[SoftImpute] Iter 34: observed MAE=0.014251 rank=4\n","[SoftImpute] Iter 35: observed MAE=0.014260 rank=4\n","[SoftImpute] Iter 36: observed MAE=0.014269 rank=4\n","[SoftImpute] Iter 37: observed MAE=0.014278 rank=4\n","[SoftImpute] Iter 38: observed MAE=0.014287 rank=4\n","[SoftImpute] Iter 39: observed MAE=0.014295 rank=4\n","[SoftImpute] Iter 40: observed MAE=0.014303 rank=4\n","[SoftImpute] Iter 41: observed MAE=0.014311 rank=4\n","[SoftImpute] Iter 42: observed MAE=0.014319 rank=4\n","[SoftImpute] Iter 43: observed MAE=0.014326 rank=4\n","[SoftImpute] Iter 44: observed MAE=0.014333 rank=4\n","[SoftImpute] Iter 45: observed MAE=0.014339 rank=4\n","[SoftImpute] Iter 46: observed MAE=0.014346 rank=4\n","[SoftImpute] Iter 47: observed MAE=0.014352 rank=4\n","[SoftImpute] Iter 48: observed MAE=0.014358 rank=4\n","[SoftImpute] Iter 49: observed MAE=0.014363 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rank=4\n","[SoftImpute] Iter 68: observed MAE=0.014437 rank=4\n","[SoftImpute] Iter 69: observed MAE=0.014439 rank=4\n","[SoftImpute] Iter 70: observed MAE=0.014442 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.014444 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.014447 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.014449 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.014451 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.014453 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.014455 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.014456 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.014458 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.014460 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.014461 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.014463 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.014464 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.014466 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.014467 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.014468 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.014469 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.014470 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.014472 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.014473 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.014474 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.014475 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.014475 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.014476 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.014477 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.014478 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.014479 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.014480 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.014480 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.014481 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.014482 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.186106\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 11508\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 9248, constraints m = 10240\n","Cones:\tprimal zero / dual free vars: 496\n","\tlinear vars: 1488\n","\tsd vars: 8256, sd blks: 1\n","Setup time: 1.38e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.22e+21  1.12e+21  1.00e+00 -7.74e+22  1.42e+22  1.92e+22  1.50e-02 \n","   100| 2.51e-03  3.20e-03  1.81e-04  1.48e+01  1.48e+01  6.83e-16  1.11e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.11e+00s\n","\tLin-sys: nnz in L factor: 31382, avg solve time: 2.34e-04s\n","\tCones: avg projection time: 7.54e-03s\n","\tAcceleration: avg step time: 2.62e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3506e-09, dist(y, K*) = 1.6069e-09, s'y/|s||y| = 2.0409e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 4.7936e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.9422e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 4.0875e-05\n","----------------------------------------------------------------------------\n","c'x = 14.8105, -b'y = 14.8117\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 9.321576\n","[SoftImpute] Iter 1: observed MAE=0.013318 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013336 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013356 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013379 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013414 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013454 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013499 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013547 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013599 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013654 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013712 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013771 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013828 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013879 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013924 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.013962 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.013999 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.014031 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.014058 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.014081 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.014102 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.014121 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.014136 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.014150 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.014162 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.014174 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.014185 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.014195 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.014206 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.014216 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.014225 rank=4\n","[SoftImpute] Iter 32: observed MAE=0.014234 rank=4\n","[SoftImpute] Iter 33: observed MAE=0.014243 rank=4\n","[SoftImpute] Iter 34: observed MAE=0.014252 rank=4\n","[SoftImpute] Iter 35: observed MAE=0.014262 rank=4\n","[SoftImpute] Iter 36: observed MAE=0.014271 rank=4\n","[SoftImpute] Iter 37: observed MAE=0.014280 rank=4\n","[SoftImpute] Iter 38: observed MAE=0.014289 rank=4\n","[SoftImpute] Iter 39: observed MAE=0.014297 rank=4\n","[SoftImpute] Iter 40: observed MAE=0.014305 rank=4\n","[SoftImpute] Iter 41: observed MAE=0.014314 rank=4\n","[SoftImpute] Iter 42: observed MAE=0.014322 rank=4\n","[SoftImpute] Iter 43: observed MAE=0.014330 rank=4\n","[SoftImpute] Iter 44: observed MAE=0.014338 rank=4\n","[SoftImpute] Iter 45: observed MAE=0.014346 rank=4\n","[SoftImpute] Iter 46: observed MAE=0.014353 rank=4\n","[SoftImpute] Iter 47: observed MAE=0.014361 rank=4\n","[SoftImpute] Iter 48: observed MAE=0.014368 rank=4\n","[SoftImpute] Iter 49: observed MAE=0.014375 rank=4\n","[SoftImpute] Iter 50: observed MAE=0.014382 rank=4\n","[SoftImpute] Iter 51: observed MAE=0.014389 rank=4\n","[SoftImpute] Iter 52: observed MAE=0.014395 rank=4\n","[SoftImpute] Iter 53: observed MAE=0.014401 rank=4\n","[SoftImpute] Iter 54: observed MAE=0.014408 rank=4\n","[SoftImpute] Iter 55: observed MAE=0.014413 rank=4\n","[SoftImpute] Iter 56: observed MAE=0.014419 rank=4\n","[SoftImpute] Iter 57: observed MAE=0.014425 rank=4\n","[SoftImpute] Iter 58: observed MAE=0.014430 rank=4\n","[SoftImpute] Iter 59: observed MAE=0.014436 rank=4\n","[SoftImpute] Iter 60: observed MAE=0.014441 rank=4\n","[SoftImpute] Iter 61: observed MAE=0.014446 rank=4\n","[SoftImpute] Iter 62: observed MAE=0.014451 rank=4\n","[SoftImpute] Iter 63: observed MAE=0.014456 rank=4\n","[SoftImpute] Iter 64: observed MAE=0.014461 rank=4\n","[SoftImpute] Iter 65: observed MAE=0.014465 rank=4\n","[SoftImpute] Iter 66: observed MAE=0.014470 rank=4\n","[SoftImpute] Iter 67: observed MAE=0.014474 rank=4\n","[SoftImpute] Iter 68: observed MAE=0.014478 rank=4\n","[SoftImpute] Iter 69: observed MAE=0.014482 rank=4\n","[SoftImpute] Iter 70: observed MAE=0.014486 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.014490 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.014494 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.014497 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.014500 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.014504 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.014507 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.014510 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.014513 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.014516 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.014518 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.014521 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.014524 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.014526 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.014529 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.014531 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.014533 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.014536 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.014538 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.014540 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.014542 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.014544 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.014546 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.014547 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.014549 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.014551 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.014552 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.014554 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.014556 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.014557 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.014559 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.186432\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 12118\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 9802, constraints m = 10826\n","Cones:\tprimal zero / dual free vars: 512\n","\tlinear vars: 1536\n","\tsd vars: 8778, sd blks: 1\n","Setup time: 1.65e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.26e+21  1.16e+21  1.00e+00 -8.26e+22  1.52e+22  2.03e+22  1.54e-02 \n","   100| 8.25e-04  1.18e-03  4.10e-04  1.53e+01  1.53e+01  1.20e-15  1.21e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.21e+00s\n","\tLin-sys: nnz in L factor: 33136, avg solve time: 2.53e-04s\n","\tCones: avg projection time: 8.38e-03s\n","\tAcceleration: avg step time: 2.76e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.6821e-09, dist(y, K*) = 1.7337e-09, s'y/|s||y| = -5.2496e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.5360e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.0654e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 4.2509e-05\n","----------------------------------------------------------------------------\n","c'x = 15.3247, -b'y = 15.3233\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 9.546894\n","[SoftImpute] Iter 1: observed MAE=0.013841 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013858 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013874 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013888 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013914 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013947 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013985 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.014028 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.014076 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.014127 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.014182 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.014238 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.014293 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.014347 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.014397 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.014444 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.014485 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.014521 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.014553 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.014581 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.014606 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.014627 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.014647 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.014666 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.014682 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.014698 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.014713 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.014728 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.014741 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.014753 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.014765 rank=4\n","[SoftImpute] Iter 32: observed MAE=0.014778 rank=4\n","[SoftImpute] Iter 33: observed MAE=0.014790 rank=4\n","[SoftImpute] Iter 34: observed MAE=0.014802 rank=4\n","[SoftImpute] Iter 35: observed MAE=0.014813 rank=4\n","[SoftImpute] Iter 36: observed MAE=0.014824 rank=4\n","[SoftImpute] Iter 37: observed MAE=0.014834 rank=4\n","[SoftImpute] Iter 38: observed MAE=0.014844 rank=4\n","[SoftImpute] Iter 39: observed MAE=0.014854 rank=4\n","[SoftImpute] Iter 40: observed MAE=0.014863 rank=4\n","[SoftImpute] Iter 41: observed MAE=0.014872 rank=4\n","[SoftImpute] Iter 42: observed MAE=0.014880 rank=4\n","[SoftImpute] Iter 43: observed MAE=0.014888 rank=4\n","[SoftImpute] Iter 44: observed MAE=0.014896 rank=4\n","[SoftImpute] Iter 45: observed MAE=0.014903 rank=4\n","[SoftImpute] Iter 46: observed MAE=0.014911 rank=4\n","[SoftImpute] Iter 47: observed MAE=0.014917 rank=4\n","[SoftImpute] Iter 48: observed MAE=0.014924 rank=4\n","[SoftImpute] Iter 49: observed MAE=0.014930 rank=4\n","[SoftImpute] Iter 50: observed MAE=0.014936 rank=4\n","[SoftImpute] Iter 51: observed MAE=0.014942 rank=4\n","[SoftImpute] Iter 52: observed MAE=0.014947 rank=4\n","[SoftImpute] Iter 53: observed MAE=0.014953 rank=4\n","[SoftImpute] Iter 54: observed MAE=0.014957 rank=4\n","[SoftImpute] Iter 55: observed MAE=0.014962 rank=4\n","[SoftImpute] Iter 56: observed MAE=0.014966 rank=4\n","[SoftImpute] Iter 57: observed MAE=0.014971 rank=4\n","[SoftImpute] Iter 58: observed MAE=0.014975 rank=4\n","[SoftImpute] Iter 59: observed MAE=0.014979 rank=4\n","[SoftImpute] Iter 60: observed MAE=0.014983 rank=4\n","[SoftImpute] Iter 61: observed MAE=0.014987 rank=4\n","[SoftImpute] Iter 62: observed MAE=0.014990 rank=4\n","[SoftImpute] Iter 63: observed MAE=0.014994 rank=4\n","[SoftImpute] Iter 64: observed MAE=0.014997 rank=4\n","[SoftImpute] Iter 65: observed MAE=0.015000 rank=4\n","[SoftImpute] Iter 66: observed MAE=0.015003 rank=4\n","[SoftImpute] Iter 67: observed MAE=0.015005 rank=4\n","[SoftImpute] Iter 68: observed MAE=0.015008 rank=4\n","[SoftImpute] Iter 69: observed MAE=0.015010 rank=4\n","[SoftImpute] Iter 70: observed MAE=0.015013 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.015015 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.015017 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.015019 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.015021 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.015022 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.015024 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.015026 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.015027 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.015029 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.015030 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.015032 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.015033 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.015034 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.015036 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.015037 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.015038 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.015039 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.015040 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.015041 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.015042 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.015043 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.015044 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.015045 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.015045 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.015046 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.015047 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.015048 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.015048 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.015049 rank=4\n","[SoftImpute] Stopped after iteration 99 for lambda=0.190938\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 10479\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 8317, constraints m = 9253\n","Cones:\tprimal zero / dual free vars: 468\n","\tlinear vars: 1404\n","\tsd vars: 7381, sd blks: 1\n","Setup time: 1.31e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.15e+21  1.06e+21  1.00e+00 -7.28e+22  1.34e+22  1.84e+22  7.81e-03 \n","   100| 1.01e-03  1.33e-03  3.57e-04  1.51e+01  1.51e+01  3.16e-15  1.06e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.06e+00s\n","\tLin-sys: nnz in L factor: 28428, avg solve time: 2.21e-04s\n","\tCones: avg projection time: 7.46e-03s\n","\tAcceleration: avg step time: 2.30e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.4645e-09, dist(y, K*) = 2.3653e-09, s'y/|s||y| = -8.6275e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.9437e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.2048e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.6074e-04\n","----------------------------------------------------------------------------\n","c'x = 15.0878, -b'y = 15.0828\n","============================================================================\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"zg2n4GjGKAp5","executionInfo":{"status":"ok","timestamp":1591370909769,"user_tz":300,"elapsed":154848,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"26912454-7cc5-470e-e57c-234a5fbca31c","colab":{"base_uri":"https://localhost:8080/","height":50}},"source":["res20"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0.02443182, 0.12466649, 0.06280594, 0.11697419, 0.16634852,\n","       0.11697419, 0.20309912])"]},"metadata":{"tags":[]},"execution_count":22}]},{"cell_type":"markdown","metadata":{"id":"gXmYvWr-BpQO"},"source":["## 30%"]},{"cell_type":"code","metadata":{"id":"bVb6Jn8O20XZ","executionInfo":{"status":"ok","timestamp":1591370918183,"user_tz":300,"elapsed":161106,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"a3e4e388-41de-4798-eedb-54daa97134a3","colab":{"base_uri":"https://localhost:8080/","height":1000}},"source":["iris = datasets.load_iris()\n","X,y = iris.data, iris.target.ravel() \n","\n","def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),25,22], [sum(ytrain==1),25,21],\n","                  [sum(ytrain==2),25,22]])\n","    p = np.array([1,3,4])    \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res30 = np.mean(np.asarray(res), axis=0)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 8.523870\n","[SoftImpute] Iter 1: observed MAE=0.013399 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013404 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013410 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013417 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013425 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013440 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013462 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013488 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013514 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013539 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013571 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013607 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013648 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013687 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013726 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.013766 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.013802 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.013835 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.013865 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.013893 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.013917 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.013939 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.013957 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.013972 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.013987 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.014001 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.014015 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.014027 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.014038 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.014049 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.014059 rank=4\n","[SoftImpute] Iter 32: observed MAE=0.014069 rank=4\n","[SoftImpute] Iter 33: observed 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MAE=0.014324 rank=4\n","[SoftImpute] Iter 70: observed MAE=0.014328 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.014332 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.014336 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.014341 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.014344 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.014348 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.014352 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.014356 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.014360 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.014364 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.014368 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.014371 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.014375 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.014378 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.014382 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.014385 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.014388 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.014391 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.014394 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.014397 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.014400 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.014403 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.014406 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.014409 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.014412 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.014414 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.014417 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.014419 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.014422 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.014424 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.014426 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.170477\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 10529\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 8447, constraints m = 9391\n","Cones:\tprimal zero / dual free vars: 472\n","\tlinear vars: 1416\n","\tsd vars: 7503, sd blks: 1\n","Setup time: 1.33e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.16e+21  1.07e+21  1.00e+00 -6.76e+22  1.25e+22  1.67e+22  1.35e-02 \n","   100| 1.08e-03  1.20e-03  1.49e-04  1.42e+01  1.42e+01  6.17e-15  1.06e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.06e+00s\n","\tLin-sys: nnz in L factor: 28700, avg solve time: 2.26e-04s\n","\tCones: avg projection time: 7.49e-03s\n","\tAcceleration: avg step time: 2.24e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3980e-09, dist(y, K*) = 1.1473e-09, s'y/|s||y| = -1.9940e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.6527e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.2482e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.3009e-04\n","----------------------------------------------------------------------------\n","c'x = 14.1654, -b'y = 14.1616\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 8.475581\n","[SoftImpute] Iter 1: observed MAE=0.013524 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013528 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013531 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013537 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013549 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013571 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013596 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013624 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013657 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013690 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013725 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013766 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013810 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013855 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013896 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.013935 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.013974 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.014009 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.014040 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.014067 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.014093 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rank=4\n","[SoftImpute] Iter 94: observed MAE=0.014577 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.014579 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.014581 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.014583 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.014584 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.014586 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.014588 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.169512\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 9819\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 7807, constraints m = 8711\n","Cones:\tprimal zero / dual free vars: 452\n","\tlinear vars: 1356\n","\tsd vars: 6903, sd blks: 1\n","Setup time: 1.75e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.11e+21  1.02e+21  1.00e+00 -6.28e+22  1.16e+22  1.57e+22  9.68e-03 \n","   100| 5.99e-04  8.27e-04  1.66e-06  1.39e+01  1.39e+01  9.16e-15  9.23e-01 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 9.23e-01s\n","\tLin-sys: nnz in L factor: 26665, avg solve time: 1.92e-04s\n","\tCones: avg projection time: 6.55e-03s\n","\tAcceleration: avg step time: 1.94e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.4195e-09, dist(y, K*) = 1.7497e-09, s'y/|s||y| = -2.1777e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.5022e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.5896e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.0166e-04\n","----------------------------------------------------------------------------\n","c'x = 13.9082, -b'y = 13.9024\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 8.444131\n","[SoftImpute] Iter 1: observed MAE=0.013148 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013152 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013158 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013166 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013176 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013186 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013195 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013212 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013232 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013255 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rank=4\n","[SoftImpute] Iter 83: observed MAE=0.013995 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.013997 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.014000 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.014002 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.014005 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.014007 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.014009 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.014012 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.014014 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.014016 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.014018 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.014020 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.014022 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.014024 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.014026 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.014028 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.014029 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.014031 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.168883\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 11414\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 9248, constraints m = 10240\n","Cones:\tprimal zero / dual free vars: 496\n","\tlinear vars: 1488\n","\tsd vars: 8256, sd blks: 1\n","Setup time: 1.66e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.21e+21  1.13e+21  1.00e+00 -7.20e+22  1.32e+22  1.75e+22  1.27e-02 \n","   100| 7.99e-04  9.28e-04  4.59e-05  1.41e+01  1.40e+01  6.36e-15  1.10e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.10e+00s\n","\tLin-sys: nnz in L factor: 31241, avg solve time: 2.24e-04s\n","\tCones: avg projection time: 7.82e-03s\n","\tAcceleration: avg step time: 2.25e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3006e-09, dist(y, K*) = 5.0884e-09, s'y/|s||y| = -9.5531e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.1908e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.3152e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.7119e-04\n","----------------------------------------------------------------------------\n","c'x = 14.0705, -b'y = 14.0784\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 8.710718\n","[SoftImpute] Iter 1: observed MAE=0.013644 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013647 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013649 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013652 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013659 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013676 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013699 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013726 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013760 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013793 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013828 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013867 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013909 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013949 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013988 rank=4\n","[SoftImpute] Iter 16: observed 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MAE=0.014413 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.014416 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.014420 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.014423 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.014427 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.014430 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.014434 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.014437 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.014440 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.014443 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.014446 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.014449 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.014452 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.014455 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.014458 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.014461 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.014463 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.014466 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.014469 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.014472 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.014474 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.014477 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.014479 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.014482 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.014484 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.014486 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.014489 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.014491 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.014493 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.014495 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.014497 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.174214\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 12024\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 9802, constraints m = 10826\n","Cones:\tprimal zero / dual free vars: 512\n","\tlinear vars: 1536\n","\tsd vars: 8778, sd blks: 1\n","Setup time: 1.60e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.26e+21  1.16e+21  1.00e+00 -7.91e+22  1.45e+22  1.90e+22  1.30e-02 \n","   100| 1.08e-03  1.22e-03  4.73e-04  1.50e+01  1.50e+01  1.98e-15  1.16e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.16e+00s\n","\tLin-sys: nnz in L factor: 32995, avg solve time: 2.45e-04s\n","\tCones: avg projection time: 8.13e-03s\n","\tAcceleration: avg step time: 2.53e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7591e-09, dist(y, K*) = 1.0772e-09, s'y/|s||y| = 2.5995e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.6449e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.4225e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 6.6247e-05\n","----------------------------------------------------------------------------\n","c'x = 14.9670, -b'y = 14.9650\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 8.837234\n","[SoftImpute] Iter 1: observed MAE=0.013980 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013988 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013996 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.014005 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.014014 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.014027 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.014048 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.014072 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.014103 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.014143 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.014185 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.014230 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.014280 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.014330 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.014378 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.014421 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.014465 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.014505 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.014545 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.014581 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.014610 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.014636 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.014659 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.014678 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.014698 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.014715 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.014731 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.014745 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.014759 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.014772 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.014784 rank=4\n","[SoftImpute] Iter 32: observed MAE=0.014795 rank=4\n","[SoftImpute] Iter 33: observed MAE=0.014806 rank=4\n","[SoftImpute] Iter 34: observed MAE=0.014816 rank=4\n","[SoftImpute] Iter 35: observed MAE=0.014827 rank=4\n","[SoftImpute] Iter 36: observed MAE=0.014837 rank=4\n","[SoftImpute] Iter 37: observed MAE=0.014847 rank=4\n","[SoftImpute] Iter 38: observed MAE=0.014857 rank=4\n","[SoftImpute] Iter 39: observed MAE=0.014866 rank=4\n","[SoftImpute] Iter 40: observed MAE=0.014876 rank=4\n","[SoftImpute] Iter 41: observed MAE=0.014885 rank=4\n","[SoftImpute] Iter 42: observed MAE=0.014895 rank=4\n","[SoftImpute] Iter 43: observed MAE=0.014904 rank=4\n","[SoftImpute] Iter 44: observed MAE=0.014914 rank=4\n","[SoftImpute] Iter 45: observed MAE=0.014923 rank=4\n","[SoftImpute] Iter 46: observed MAE=0.014931 rank=4\n","[SoftImpute] Iter 47: observed MAE=0.014940 rank=4\n","[SoftImpute] Iter 48: observed MAE=0.014948 rank=4\n","[SoftImpute] Iter 49: observed MAE=0.014956 rank=4\n","[SoftImpute] Iter 50: observed MAE=0.014964 rank=4\n","[SoftImpute] Iter 51: observed MAE=0.014972 rank=4\n","[SoftImpute] Iter 52: observed MAE=0.014980 rank=4\n","[SoftImpute] Iter 53: observed MAE=0.014987 rank=4\n","[SoftImpute] Iter 54: observed MAE=0.014995 rank=4\n","[SoftImpute] Iter 55: observed MAE=0.015002 rank=4\n","[SoftImpute] Iter 56: observed MAE=0.015009 rank=4\n","[SoftImpute] Iter 57: observed MAE=0.015015 rank=4\n","[SoftImpute] Iter 58: observed MAE=0.015022 rank=4\n","[SoftImpute] Iter 59: observed MAE=0.015029 rank=4\n","[SoftImpute] Iter 60: observed MAE=0.015035 rank=4\n","[SoftImpute] Iter 61: observed MAE=0.015042 rank=4\n","[SoftImpute] Iter 62: observed MAE=0.015048 rank=4\n","[SoftImpute] Iter 63: observed MAE=0.015055 rank=4\n","[SoftImpute] Iter 64: observed MAE=0.015061 rank=4\n","[SoftImpute] Iter 65: observed MAE=0.015067 rank=4\n","[SoftImpute] Iter 66: observed MAE=0.015072 rank=4\n","[SoftImpute] Iter 67: observed MAE=0.015078 rank=4\n","[SoftImpute] Iter 68: observed MAE=0.015083 rank=4\n","[SoftImpute] Iter 69: observed MAE=0.015088 rank=4\n","[SoftImpute] Iter 70: observed MAE=0.015094 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.015099 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.015104 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.015109 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.015114 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.015118 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.015122 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.015127 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.015131 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.015135 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.015139 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.015143 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.015146 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.015150 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.015153 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.015156 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.015160 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.015163 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.015166 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.015168 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.015171 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.015174 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.015176 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.015179 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.015181 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.015183 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.015186 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.015188 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.015190 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.015192 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.015194 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.176745\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 10385\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 8317, constraints m = 9253\n","Cones:\tprimal zero / dual free vars: 468\n","\tlinear vars: 1404\n","\tsd vars: 7381, sd blks: 1\n","Setup time: 1.32e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.15e+21  1.06e+21  1.00e+00 -6.91e+22  1.28e+22  1.71e+22  1.41e-02 \n","   100| 1.51e-03  2.01e-03  1.22e-04  1.45e+01  1.46e+01  2.01e-15  1.00e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.00e+00s\n","\tLin-sys: nnz in L factor: 28287, avg solve time: 2.04e-04s\n","\tCones: avg projection time: 7.14e-03s\n","\tAcceleration: avg step time: 2.06e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.4894e-09, dist(y, K*) = 1.3977e-09, s'y/|s||y| = 4.0573e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.5561e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.4066e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.0350e-04\n","----------------------------------------------------------------------------\n","c'x = 14.5263, -b'y = 14.5202\n","============================================================================\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"Y170hDMgKfwU","executionInfo":{"status":"ok","timestamp":1591370918187,"user_tz":300,"elapsed":160121,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"cab4b08a-8507-4556-862c-6a02b8b5e7d6","colab":{"base_uri":"https://localhost:8080/","height":50}},"source":["res30"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0.03212413, 0.15534831, 0.06280594, 0.12625449, 0.15329451,\n","       0.1353454 , 0.3012073 ])"]},"metadata":{"tags":[]},"execution_count":24}]},{"cell_type":"markdown","metadata":{"id":"Fie3E5JwCWqo"},"source":["## 40%"]},{"cell_type":"code","metadata":{"id":"WeVyilQIaaEF","executionInfo":{"status":"ok","timestamp":1604556899912,"user_tz":360,"elapsed":9711,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"d98226d4-b9a3-4e17-f093-d927ace28f55","colab":{"base_uri":"https://localhost:8080/"}},"source":["iris = datasets.load_iris()\n","X,y = iris.data, iris.target.ravel() \n","\n","def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),20,15], [sum(ytrain==1),20,15],\n","                  [sum(ytrain==2),20,16]])\n","    p = np.array([1,3,4])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res40 = np.mean(np.asarray(res), axis=0)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 7.596066\n","[SoftImpute] Iter 1: observed MAE=0.013298 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013297 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013294 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013290 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013286 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013280 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013273 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013265 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013258 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013252 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013255 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013262 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013274 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013287 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013302 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.013318 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.013338 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.013357 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.013377 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.013396 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.013416 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.013437 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.013458 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.013478 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.013497 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.013514 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.013532 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.013552 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.013569 rank=4\n","[SoftImpute] Iter 30: observed 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MAE=0.013784 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.013786 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.013788 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.013790 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.013792 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.013794 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.013796 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.013798 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.013800 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.013802 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.013804 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.013806 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.013807 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.013809 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.013811 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.013813 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.013815 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.151921\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 10431\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 8447, constraints m = 9391\n","Cones:\tprimal zero / dual free vars: 472\n","\tlinear vars: 1416\n","\tsd vars: 7503, sd blks: 1\n","Setup time: 1.24e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.16e+21  1.07e+21  1.00e+00 -6.27e+22  1.16e+22  1.51e+22  7.01e-03 \n","   100| 7.96e-04  1.11e-03  3.17e-04  1.36e+01  1.36e+01  4.37e-15  1.08e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.08e+00s\n","\tLin-sys: nnz in L factor: 28553, avg solve time: 2.22e-04s\n","\tCones: avg projection time: 7.67e-03s\n","\tAcceleration: avg step time: 2.30e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.5054e-09, dist(y, K*) = 1.4269e-09, s'y/|s||y| = -4.3851e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.2301e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.5441e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.8448e-05\n","----------------------------------------------------------------------------\n","c'x = 13.5968, -b'y = 13.5976\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 7.568424\n","[SoftImpute] Iter 1: observed MAE=0.013490 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013487 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013483 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013478 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013472 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013466 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013461 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013457 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013453 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013455 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013459 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013472 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013487 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013502 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013516 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.013530 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.013546 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.013564 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.013587 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.013613 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.013637 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.013660 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.013683 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.013705 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.013728 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.013750 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.013773 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.013794 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.013813 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.013830 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.013845 rank=4\n","[SoftImpute] Iter 32: observed MAE=0.013859 rank=4\n","[SoftImpute] Iter 33: observed MAE=0.013870 rank=4\n","[SoftImpute] Iter 34: observed MAE=0.013880 rank=4\n","[SoftImpute] Iter 35: observed MAE=0.013888 rank=4\n","[SoftImpute] Iter 36: observed MAE=0.013896 rank=4\n","[SoftImpute] Iter 37: observed MAE=0.013903 rank=4\n","[SoftImpute] Iter 38: observed MAE=0.013910 rank=4\n","[SoftImpute] Iter 39: observed MAE=0.013918 rank=4\n","[SoftImpute] Iter 40: observed MAE=0.013924 rank=4\n","[SoftImpute] Iter 41: observed MAE=0.013929 rank=4\n","[SoftImpute] Iter 42: observed MAE=0.013934 rank=4\n","[SoftImpute] Iter 43: observed MAE=0.013939 rank=4\n","[SoftImpute] Iter 44: observed MAE=0.013944 rank=4\n","[SoftImpute] Iter 45: observed MAE=0.013948 rank=4\n","[SoftImpute] Iter 46: observed MAE=0.013951 rank=4\n","[SoftImpute] Iter 47: observed MAE=0.013954 rank=4\n","[SoftImpute] Iter 48: observed MAE=0.013957 rank=4\n","[SoftImpute] Iter 49: observed MAE=0.013960 rank=4\n","[SoftImpute] Iter 50: observed MAE=0.013964 rank=4\n","[SoftImpute] Iter 51: observed MAE=0.013967 rank=4\n","[SoftImpute] Iter 52: observed MAE=0.013970 rank=4\n","[SoftImpute] Iter 53: observed MAE=0.013973 rank=4\n","[SoftImpute] Iter 54: observed MAE=0.013975 rank=4\n","[SoftImpute] Iter 55: observed MAE=0.013978 rank=4\n","[SoftImpute] Iter 56: observed MAE=0.013981 rank=4\n","[SoftImpute] Iter 57: observed MAE=0.013984 rank=4\n","[SoftImpute] Iter 58: observed MAE=0.013988 rank=4\n","[SoftImpute] Iter 59: observed MAE=0.013991 rank=4\n","[SoftImpute] Iter 60: observed MAE=0.013994 rank=4\n","[SoftImpute] Iter 61: observed MAE=0.013997 rank=4\n","[SoftImpute] Iter 62: observed MAE=0.014000 rank=4\n","[SoftImpute] Iter 63: observed MAE=0.014002 rank=4\n","[SoftImpute] Iter 64: observed MAE=0.014005 rank=4\n","[SoftImpute] Iter 65: observed MAE=0.014008 rank=4\n","[SoftImpute] Iter 66: observed MAE=0.014011 rank=4\n","[SoftImpute] Iter 67: observed MAE=0.014013 rank=4\n","[SoftImpute] Iter 68: observed MAE=0.014016 rank=4\n","[SoftImpute] Iter 69: observed MAE=0.014018 rank=4\n","[SoftImpute] Iter 70: observed MAE=0.014021 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.014023 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.014026 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.014028 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.014030 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.014033 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.014035 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.014037 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.014039 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.014042 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.014044 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.014046 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.014048 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.014050 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.014052 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.014054 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.014056 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.014059 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.014061 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.014063 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.014065 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.014068 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.014070 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.014072 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.014074 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.014077 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.014079 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.014081 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.014083 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.014085 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.014088 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.151368\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 9721\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 7807, constraints m = 8711\n","Cones:\tprimal zero / dual free vars: 452\n","\tlinear vars: 1356\n","\tsd vars: 6903, sd blks: 1\n","Setup time: 1.20e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.11e+21  1.03e+21  1.00e+00 -5.80e+22  1.07e+22  1.42e+22  1.39e-02 \n","   100| 9.71e-04  1.79e-03  5.50e-05  1.32e+01  1.32e+01  3.92e-16  9.62e-01 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 9.62e-01s\n","\tLin-sys: nnz in L factor: 26518, avg solve time: 2.03e-04s\n","\tCones: avg projection time: 6.69e-03s\n","\tAcceleration: avg step time: 2.10e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3131e-09, dist(y, K*) = 3.4722e-09, s'y/|s||y| = -4.7038e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.3083e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.5673e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.7859e-04\n","----------------------------------------------------------------------------\n","c'x = 13.2180, -b'y = 13.2104\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 7.476328\n","[SoftImpute] Iter 1: observed MAE=0.012935 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.012933 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.012930 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.012926 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.012920 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.012913 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.012907 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.012900 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.012894 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.012890 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.012888 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.012889 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.012889 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.012889 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.012888 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.012892 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.012899 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.012907 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.012919 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.012932 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.012948 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.012968 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.012988 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.013005 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.013021 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rank=4\n","[SoftImpute] Iter 62: observed MAE=0.013165 rank=4\n","[SoftImpute] Iter 63: observed MAE=0.013168 rank=4\n","[SoftImpute] Iter 64: observed MAE=0.013170 rank=4\n","[SoftImpute] Iter 65: observed MAE=0.013172 rank=4\n","[SoftImpute] Iter 66: observed MAE=0.013174 rank=4\n","[SoftImpute] Iter 67: observed MAE=0.013176 rank=4\n","[SoftImpute] Iter 68: observed MAE=0.013178 rank=4\n","[SoftImpute] Iter 69: observed MAE=0.013180 rank=4\n","[SoftImpute] Iter 70: observed MAE=0.013182 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.013184 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.013185 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.013187 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.013189 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.013191 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.013192 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.013194 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.013196 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.013197 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.013199 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.013200 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.013202 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.013204 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.013205 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.013207 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.013209 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.013210 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.013212 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.013213 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.013215 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.013216 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.013218 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.013219 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.013221 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.013222 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.013223 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.013225 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.013226 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.013228 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.013229 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.149527\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 11316\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 9248, constraints m = 10240\n","Cones:\tprimal zero / dual free vars: 496\n","\tlinear vars: 1488\n","\tsd vars: 8256, sd blks: 1\n","Setup time: 1.61e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.21e+21  1.13e+21  1.00e+00 -6.64e+22  1.22e+22  1.58e+22  1.60e-02 \n","   100| 8.27e-04  1.22e-03  3.30e-04  1.34e+01  1.34e+01  2.96e-15  1.12e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.12e+00s\n","\tLin-sys: nnz in L factor: 31094, avg solve time: 2.37e-04s\n","\tCones: avg projection time: 7.62e-03s\n","\tAcceleration: avg step time: 2.68e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.2741e-09, dist(y, K*) = 1.4644e-09, s'y/|s||y| = -3.1979e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.0552e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.2833e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.8362e-04\n","----------------------------------------------------------------------------\n","c'x = 13.3984, -b'y = 13.3905\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 7.770949\n","[SoftImpute] Iter 1: observed MAE=0.013371 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013370 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013369 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013366 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013363 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013359 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013356 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013355 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013355 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013355 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013358 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013366 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013377 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013389 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013402 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.013415 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.013435 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.013458 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.013481 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.013504 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.013526 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.013548 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.013570 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.013592 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.013613 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.013632 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.013650 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.013665 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.013679 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.013694 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.013710 rank=4\n","[SoftImpute] Iter 32: observed 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MAE=0.013866 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.013868 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.013870 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.013872 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.013874 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.013876 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.013878 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.013880 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.013881 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.013883 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.013885 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.013887 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.013889 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.013891 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.013892 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.155419\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 11926\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 9802, constraints m = 10826\n","Cones:\tprimal zero / dual free vars: 512\n","\tlinear vars: 1536\n","\tsd vars: 8778, sd blks: 1\n","Setup time: 1.60e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.25e+21  1.17e+21  1.00e+00 -7.34e+22  1.35e+22  1.73e+22  1.63e-02 \n","   100| 1.89e-03  2.71e-03  1.51e-04  1.43e+01  1.43e+01  4.05e-16  1.19e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.19e+00s\n","\tLin-sys: nnz in L factor: 32848, avg solve time: 2.46e-04s\n","\tCones: avg projection time: 8.25e-03s\n","\tAcceleration: avg step time: 2.65e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.8641e-09, dist(y, K*) = 1.4818e-09, s'y/|s||y| = -3.3537e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.1285e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 1.5741e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.1052e-04\n","----------------------------------------------------------------------------\n","c'x = 14.3252, -b'y = 14.3189\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 7.925653\n","[SoftImpute] Iter 1: observed MAE=0.013941 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013941 rank=4\n","[SoftImpute] Iter 3: 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MAE=0.014335 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.014339 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.014342 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.014346 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.014350 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.014354 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.014358 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.014361 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.014365 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.014369 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.014372 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.014376 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.014379 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.014382 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.014385 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.014389 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.014392 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.014395 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.014398 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.014401 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.014404 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.014407 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.014410 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.014412 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.014415 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.014418 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.158513\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 10287\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 8317, constraints m = 9253\n","Cones:\tprimal zero / dual free vars: 468\n","\tlinear vars: 1404\n","\tsd vars: 7381, sd blks: 1\n","Setup time: 1.22e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.15e+21  1.06e+21  1.00e+00 -6.41e+22  1.18e+22  1.55e+22  1.23e-02 \n","   100| 7.13e-04  7.44e-04  2.76e-05  1.38e+01  1.38e+01  6.51e-15  1.07e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.07e+00s\n","\tLin-sys: nnz in L factor: 28140, avg solve time: 2.13e-04s\n","\tCones: avg projection time: 7.55e-03s\n","\tAcceleration: avg step time: 2.37e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3531e-09, dist(y, K*) = 1.6995e-09, s'y/|s||y| = -6.4486e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.0598e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 1.7080e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.1980e-04\n","----------------------------------------------------------------------------\n","c'x = 13.8471, -b'y = 13.8408\n","============================================================================\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"za2O4bZaJ0mi","executionInfo":{"status":"ok","timestamp":1604556899916,"user_tz":360,"elapsed":8576,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"21f61042-b753-45a1-a53a-bd3f5dd64fa5","colab":{"base_uri":"https://localhost:8080/"}},"source":["res40"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0.03697552, 0.15329451, 0.07511655, 0.13250449, 0.16382773,\n","       0.13250449, 0.40349028])"]},"metadata":{"tags":[]},"execution_count":56}]},{"cell_type":"code","metadata":{"id":"Lzh0CvE5axI7","executionInfo":{"status":"ok","timestamp":1591370926781,"user_tz":300,"elapsed":164194,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"4b2cf3ac-5dea-49c3-d543-318361fdfd95","colab":{"base_uri":"https://localhost:8080/","height":118}},"source":["iris = np.vstack((res20, res30, res40))\n","iris"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[0.02443182, 0.12466649, 0.06280594, 0.11697419, 0.16634852,\n","        0.11697419, 0.20309912],\n","       [0.03212413, 0.15534831, 0.06280594, 0.12625449, 0.15329451,\n","        0.1353454 , 0.3012073 ],\n","       [0.03697552, 0.15329451, 0.07511655, 0.13250449, 0.16382773,\n","        0.13250449, 0.40349028]])"]},"metadata":{"tags":[]},"execution_count":27}]},{"cell_type":"markdown","metadata":{"id":"95RaxVupBp2Z"},"source":["## 50%"]},{"cell_type":"code","metadata":{"id":"BrW4v3y7BrXH","executionInfo":{"status":"ok","timestamp":1604558147688,"user_tz":360,"elapsed":10836,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"c1da87f0-0297-4dee-f837-3d97763649cb","colab":{"base_uri":"https://localhost:8080/"}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    n = np.array([[sum(ytrain==0),16,9], [sum(ytrain==1),16,9],\n","                  [sum(ytrain==2),15,8]])\n","    p = np.array([1,3,4])\n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","\n","# cross_validation error\n","res = [fold_k_err(X,y,k,3) for k in np.arange(5)]\n","res50 = np.mean(np.asarray(res), axis=0)    "],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 6.563806\n","[SoftImpute] Iter 1: observed MAE=0.012793 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.012791 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.012789 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.012787 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.012784 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.012781 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.012778 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.012773 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.012769 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.012765 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.012761 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.012756 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.012750 rank=4\n","[SoftImpute] Iter 14: observed 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ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 10339\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 8447, constraints m = 9391\n","Cones:\tprimal zero / dual free vars: 472\n","\tlinear vars: 1416\n","\tsd vars: 7503, sd blks: 1\n","Setup time: 1.24e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.15e+21  1.08e+21  1.00e+00 -5.66e+22  1.04e+22  1.34e+22  1.02e-02 \n","   100| 2.26e-03  2.65e-03  1.54e-05  1.26e+01  1.26e+01  1.56e-15  1.07e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.07e+00s\n","\tLin-sys: nnz in L factor: 28415, avg solve time: 2.15e-04s\n","\tCones: avg projection time: 7.52e-03s\n","\tAcceleration: avg step time: 2.36e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1365e-09, dist(y, K*) = 1.7780e-09, s'y/|s||y| = 1.2995e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.1145e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.4184e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 5.4825e-05\n","----------------------------------------------------------------------------\n","c'x = 12.6257, -b'y = 12.6242\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 6.550036\n","[SoftImpute] Iter 1: observed MAE=0.013159 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013155 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013152 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013148 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013143 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013138 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013132 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013126 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013119 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013111 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013104 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013096 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013088 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013079 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013071 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.013063 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.013054 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.013046 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.013038 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.013030 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.013022 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.013014 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.013005 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.012999 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.012994 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.012989 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.012984 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.012980 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.012977 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.012974 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.012971 rank=4\n","[SoftImpute] Iter 32: observed 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ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 9629\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 7807, constraints m = 8711\n","Cones:\tprimal zero / dual free vars: 452\n","\tlinear vars: 1356\n","\tsd vars: 6903, sd blks: 1\n","Setup time: 1.37e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.10e+21  1.03e+21  1.00e+00 -5.27e+22  9.77e+21  1.26e+22  1.36e-02 \n","   100| 2.39e-03  3.32e-03  3.63e-04  1.25e+01  1.26e+01  1.40e-15  9.84e-01 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 9.84e-01s\n","\tLin-sys: nnz in L factor: 26380, avg solve time: 1.98e-04s\n","\tCones: avg projection time: 6.81e-03s\n","\tAcceleration: avg step time: 2.26e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1956e-09, dist(y, K*) = 1.7302e-09, s'y/|s||y| = 2.7602e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.8636e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.2583e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 9.9010e-05\n","----------------------------------------------------------------------------\n","c'x = 12.5374, -b'y = 12.5348\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 6.402702\n","[SoftImpute] Iter 1: observed MAE=0.012378 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.012378 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.012377 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.012376 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.012374 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.012371 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.012368 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.012364 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.012359 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.012354 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.012349 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.012342 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.012335 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.012328 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.012320 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.012311 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.012302 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.012293 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.012283 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.012273 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.012264 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.012254 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.012244 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.012238 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.012235 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.012233 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.012230 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.012227 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.012224 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.012222 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.012221 rank=4\n","[SoftImpute] Iter 32: observed 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ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 11224\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 9248, constraints m = 10240\n","Cones:\tprimal zero / dual free vars: 496\n","\tlinear vars: 1488\n","\tsd vars: 8256, sd blks: 1\n","Setup time: 1.31e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.21e+21  1.13e+21  1.00e+00 -5.95e+22  1.09e+22  1.39e+22  1.46e-02 \n","   100| 9.66e-04  1.35e-03  5.53e-05  1.24e+01  1.24e+01  2.36e-15  1.10e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.10e+00s\n","\tLin-sys: nnz in L factor: 30956, avg solve time: 2.30e-04s\n","\tCones: avg projection time: 7.60e-03s\n","\tAcceleration: avg step time: 2.50e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.3411e-09, dist(y, K*) = 3.4002e-09, s'y/|s||y| = 1.2034e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.7951e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.1613e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.8269e-04\n","----------------------------------------------------------------------------\n","c'x = 12.4099, -b'y = 12.4026\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 6.830553\n","[SoftImpute] Iter 1: observed MAE=0.013107 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013105 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013102 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013098 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013094 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013090 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013086 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013081 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013077 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013072 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013066 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013059 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013052 rank=4\n","[SoftImpute] Iter 14: 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ConvergenceWarning: [IterativeImputer] Early stopping criterion not reached.\n","  \" reached.\", ConvergenceWarning)\n"],"name":"stderr"},{"output_type":"stream","text":["----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 11834\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 9802, constraints m = 10826\n","Cones:\tprimal zero / dual free vars: 512\n","\tlinear vars: 1536\n","\tsd vars: 8778, sd blks: 1\n","Setup time: 1.32e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.25e+21  1.17e+21  1.00e+00 -6.66e+22  1.22e+22  1.54e+22  1.61e-02 \n","   100| 1.09e-03  1.77e-03  2.71e-04  1.33e+01  1.33e+01  3.68e-15  1.22e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.22e+00s\n","\tLin-sys: nnz in L factor: 32710, avg solve time: 2.46e-04s\n","\tCones: avg projection time: 8.41e-03s\n","\tAcceleration: avg step time: 2.70e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.7861e-09, dist(y, K*) = 1.3956e-09, s'y/|s||y| = 3.4231e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.7782e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.3041e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 3.8855e-04\n","----------------------------------------------------------------------------\n","c'x = 13.2599, -b'y = 13.2492\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 6.981715\n","[SoftImpute] Iter 1: observed MAE=0.013790 rank=4\n","[SoftImpute] Iter 2: observed MAE=0.013791 rank=4\n","[SoftImpute] Iter 3: observed MAE=0.013791 rank=4\n","[SoftImpute] Iter 4: observed MAE=0.013791 rank=4\n","[SoftImpute] Iter 5: observed MAE=0.013789 rank=4\n","[SoftImpute] Iter 6: observed MAE=0.013788 rank=4\n","[SoftImpute] Iter 7: observed MAE=0.013785 rank=4\n","[SoftImpute] Iter 8: observed MAE=0.013781 rank=4\n","[SoftImpute] Iter 9: observed MAE=0.013777 rank=4\n","[SoftImpute] Iter 10: observed MAE=0.013772 rank=4\n","[SoftImpute] Iter 11: observed MAE=0.013767 rank=4\n","[SoftImpute] Iter 12: observed MAE=0.013760 rank=4\n","[SoftImpute] Iter 13: observed MAE=0.013753 rank=4\n","[SoftImpute] Iter 14: observed MAE=0.013745 rank=4\n","[SoftImpute] Iter 15: observed MAE=0.013739 rank=4\n","[SoftImpute] Iter 16: observed MAE=0.013732 rank=4\n","[SoftImpute] Iter 17: observed MAE=0.013726 rank=4\n","[SoftImpute] Iter 18: observed MAE=0.013719 rank=4\n","[SoftImpute] Iter 19: observed MAE=0.013714 rank=4\n","[SoftImpute] Iter 20: observed MAE=0.013709 rank=4\n","[SoftImpute] Iter 21: observed MAE=0.013705 rank=4\n","[SoftImpute] Iter 22: observed MAE=0.013706 rank=4\n","[SoftImpute] Iter 23: observed MAE=0.013706 rank=4\n","[SoftImpute] Iter 24: observed MAE=0.013706 rank=4\n","[SoftImpute] Iter 25: observed MAE=0.013708 rank=4\n","[SoftImpute] Iter 26: observed MAE=0.013710 rank=4\n","[SoftImpute] Iter 27: observed MAE=0.013712 rank=4\n","[SoftImpute] Iter 28: observed MAE=0.013717 rank=4\n","[SoftImpute] Iter 29: observed MAE=0.013723 rank=4\n","[SoftImpute] Iter 30: observed MAE=0.013729 rank=4\n","[SoftImpute] Iter 31: observed MAE=0.013738 rank=4\n","[SoftImpute] Iter 32: observed MAE=0.013746 rank=4\n","[SoftImpute] Iter 33: observed MAE=0.013754 rank=4\n","[SoftImpute] Iter 34: observed MAE=0.013762 rank=4\n","[SoftImpute] Iter 35: observed MAE=0.013769 rank=4\n","[SoftImpute] Iter 36: observed MAE=0.013777 rank=4\n","[SoftImpute] Iter 37: observed MAE=0.013785 rank=4\n","[SoftImpute] Iter 38: observed MAE=0.013793 rank=4\n","[SoftImpute] Iter 39: observed MAE=0.013800 rank=4\n","[SoftImpute] Iter 40: observed MAE=0.013806 rank=4\n","[SoftImpute] Iter 41: observed MAE=0.013812 rank=4\n","[SoftImpute] Iter 42: observed MAE=0.013818 rank=4\n","[SoftImpute] Iter 43: observed MAE=0.013823 rank=4\n","[SoftImpute] Iter 44: observed MAE=0.013827 rank=4\n","[SoftImpute] Iter 45: observed MAE=0.013832 rank=4\n","[SoftImpute] Iter 46: observed MAE=0.013836 rank=4\n","[SoftImpute] Iter 47: observed MAE=0.013841 rank=4\n","[SoftImpute] Iter 48: observed MAE=0.013845 rank=4\n","[SoftImpute] Iter 49: observed MAE=0.013849 rank=4\n","[SoftImpute] Iter 50: observed MAE=0.013852 rank=4\n","[SoftImpute] Iter 51: observed MAE=0.013855 rank=4\n","[SoftImpute] Iter 52: observed MAE=0.013858 rank=4\n","[SoftImpute] Iter 53: observed MAE=0.013861 rank=4\n","[SoftImpute] Iter 54: observed MAE=0.013864 rank=4\n","[SoftImpute] Iter 55: observed MAE=0.013866 rank=4\n","[SoftImpute] Iter 56: observed MAE=0.013869 rank=4\n","[SoftImpute] Iter 57: observed MAE=0.013871 rank=4\n","[SoftImpute] Iter 58: observed MAE=0.013872 rank=4\n","[SoftImpute] Iter 59: observed MAE=0.013874 rank=4\n","[SoftImpute] Iter 60: observed MAE=0.013875 rank=4\n","[SoftImpute] Iter 61: observed MAE=0.013876 rank=4\n","[SoftImpute] Iter 62: observed MAE=0.013877 rank=4\n","[SoftImpute] Iter 63: observed MAE=0.013878 rank=4\n","[SoftImpute] Iter 64: observed MAE=0.013879 rank=4\n","[SoftImpute] Iter 65: observed MAE=0.013880 rank=4\n","[SoftImpute] Iter 66: observed MAE=0.013881 rank=4\n","[SoftImpute] Iter 67: observed MAE=0.013881 rank=4\n","[SoftImpute] Iter 68: observed MAE=0.013882 rank=4\n","[SoftImpute] Iter 69: observed MAE=0.013882 rank=4\n","[SoftImpute] Iter 70: observed MAE=0.013883 rank=4\n","[SoftImpute] Iter 71: observed MAE=0.013883 rank=4\n","[SoftImpute] Iter 72: observed MAE=0.013884 rank=4\n","[SoftImpute] Iter 73: observed MAE=0.013885 rank=4\n","[SoftImpute] Iter 74: observed MAE=0.013885 rank=4\n","[SoftImpute] Iter 75: observed MAE=0.013886 rank=4\n","[SoftImpute] Iter 76: observed MAE=0.013886 rank=4\n","[SoftImpute] Iter 77: observed MAE=0.013887 rank=4\n","[SoftImpute] Iter 78: observed MAE=0.013887 rank=4\n","[SoftImpute] Iter 79: observed MAE=0.013887 rank=4\n","[SoftImpute] Iter 80: observed MAE=0.013888 rank=4\n","[SoftImpute] Iter 81: observed MAE=0.013888 rank=4\n","[SoftImpute] Iter 82: observed MAE=0.013888 rank=4\n","[SoftImpute] Iter 83: observed MAE=0.013889 rank=4\n","[SoftImpute] Iter 84: observed MAE=0.013889 rank=4\n","[SoftImpute] Iter 85: observed MAE=0.013889 rank=4\n","[SoftImpute] Iter 86: observed MAE=0.013890 rank=4\n","[SoftImpute] Iter 87: observed MAE=0.013890 rank=4\n","[SoftImpute] Iter 88: observed MAE=0.013890 rank=4\n","[SoftImpute] Iter 89: observed MAE=0.013890 rank=4\n","[SoftImpute] Iter 90: observed MAE=0.013891 rank=4\n","[SoftImpute] Iter 91: observed MAE=0.013891 rank=4\n","[SoftImpute] Iter 92: observed MAE=0.013892 rank=4\n","[SoftImpute] Iter 93: observed MAE=0.013892 rank=4\n","[SoftImpute] Iter 94: observed MAE=0.013893 rank=4\n","[SoftImpute] Iter 95: observed MAE=0.013893 rank=4\n","[SoftImpute] Iter 96: observed MAE=0.013894 rank=4\n","[SoftImpute] Iter 97: observed MAE=0.013895 rank=4\n","[SoftImpute] Iter 98: observed MAE=0.013896 rank=4\n","[SoftImpute] Iter 99: observed MAE=0.013896 rank=4\n","[SoftImpute] Iter 100: observed MAE=0.013897 rank=4\n","[SoftImpute] Stopped after iteration 100 for lambda=0.139634\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 10195\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 8317, constraints m = 9253\n","Cones:\tprimal zero / dual free vars: 468\n","\tlinear vars: 1404\n","\tsd vars: 7381, sd blks: 1\n","Setup time: 1.71e-02s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.15e+21  1.07e+21  1.00e+00 -5.84e+22  1.08e+22  1.38e+22  1.29e-02 \n","   100| 2.07e-04  2.37e-04  6.33e-06  1.30e+01  1.30e+01  1.92e-15  1.02e+00 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 1.02e+00s\n","\tLin-sys: nnz in L factor: 28002, avg solve time: 2.08e-04s\n","\tCones: avg projection time: 7.12e-03s\n","\tAcceleration: avg step time: 2.23e-03s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.1112e-09, dist(y, K*) = 1.2825e-09, s'y/|s||y| = 1.2282e-12\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.0746e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 2.3691e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 6.3251e-06\n","----------------------------------------------------------------------------\n","c'x = 12.9918, -b'y = 12.9916\n","============================================================================\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"k_7PrDfnChvF","executionInfo":{"status":"ok","timestamp":1604558147690,"user_tz":360,"elapsed":7784,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"e8379aab-fb2a-40db-9381-d604e0094f77","colab":{"base_uri":"https://localhost:8080/"}},"source":["res50"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0.04587704, 0.20057015, 0.1354021 , 0.14284831, 0.21044817,\n","       0.14568922, 0.49951105])"]},"metadata":{"tags":[]},"execution_count":94}]},{"cell_type":"code","metadata":{"id":"SRB0M-UrD-7p"},"source":[""],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"yHtyE8f2_yKK"},"source":["# Digits"]},{"cell_type":"code","metadata":{"id":"ke4friFzAOp0","executionInfo":{"status":"ok","timestamp":1604558261899,"user_tz":360,"elapsed":894,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"595cf22f-7c3c-45c1-bf0c-e42e4d57fa91","colab":{"base_uri":"https://localhost:8080/"}},"source":["digits = datasets.load_digits()\n","X,y = digits.data, digits.target.ravel() \n","print(X.shape)\n","rmid = np.where(sum(X!=0)<10)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["(1797, 64)\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"ZHTX4SLcDWSV","executionInfo":{"status":"ok","timestamp":1604558262166,"user_tz":360,"elapsed":476,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"3e620132-44f1-40a3-bbda-2b2c2c90ba95","colab":{"base_uri":"https://localhost:8080/"}},"source":["X = np.delete(X, rmid,axis = 1)\n","X.shape"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(1797, 54)"]},"metadata":{"tags":[]},"execution_count":96}]},{"cell_type":"markdown","metadata":{"id":"idCSgJbTrgvm"},"source":["## 20%"]},{"cell_type":"code","metadata":{"id":"MPe3MA5D_z_G"},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    ng = np.asarray([sum(ytrain==i) for i in np.arange(10)])\n","    n = np.hstack((ng.reshape((-1,1)), np.tile([125,120,100, 90],\n","                                 10).reshape((10,-1))))\n","    p = np.array([10,19, 25,56])    \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,10) for k in np.arange(5)]\n","res20 = np.mean(np.asarray(res), axis=0)"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"ootPRoaxwgEr","executionInfo":{"status":"ok","timestamp":1590281895175,"user_tz":300,"elapsed":86,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"0b64ddf0-6542-494f-8295-8bb4803c91db","colab":{"base_uri":"https://localhost:8080/","height":50}},"source":["res20"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0.05752231, 0.07124877, 0.07087817, 0.07022853, 0.06020288,\n","       0.0696683 , 0.07087817, 0.06966812, 0.20354437])"]},"metadata":{"tags":[]},"execution_count":12}]},{"cell_type":"markdown","metadata":{"id":"ONIR0QB7rkqv"},"source":["## 30%"]},{"cell_type":"code","metadata":{"id":"vyTfBT-Y3Uoz"},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    ng = np.asarray([sum(ytrain==i) for i in np.arange(10)])\n","    n = np.hstack((ng.reshape((-1,1)), np.tile([130,115,90, 80,70,60],\n","                                 10).reshape((10,-1))))\n","    p = np.array([10,15, 25,30,40,56]) \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,10) for k in np.arange(5)]\n","res30 = np.mean(np.asarray(res), axis=0)"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"I6r7I5HKIhlW","executionInfo":{"status":"ok","timestamp":1590230659600,"user_tz":300,"elapsed":1819,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"da52fe1e-00ea-41b6-ddb8-a12375b3cdf9","colab":{"base_uri":"https://localhost:8080/","height":50}},"source":["res30"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0.05783407, 0.08195374, 0.06966223, 0.07142643, 0.06357481,\n","       0.07195977, 0.06856867, 0.07519163, 0.29565362])"]},"metadata":{"tags":[]},"execution_count":185}]},{"cell_type":"markdown","metadata":{"id":"bZY1k465vA6t"},"source":["## 40%"]},{"cell_type":"code","metadata":{"id":"KYUM1-_L3-eQ"},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    ng = np.asarray([sum(ytrain==i) for i in np.arange(10)])\n","    n = np.hstack((ng.reshape((-1,1)), np.tile([110,100,80, 70,55,50],\n","                                 10).reshape((10,-1))))\n","    p = np.array([10,12, 20,27,35,56]) \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,10) for k in np.arange(5)]\n","res40 = np.mean(np.asarray(res), axis=0)"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"x12FtB5RpT1u"},"source":["digits = np.vstack((res20,res30,res40))\n","digits"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"DI-C6ND2IDxK"},"source":["## 50%"]},{"cell_type":"code","metadata":{"id":"w0uvtrYJIFZx","executionInfo":{"status":"ok","timestamp":1604561966405,"user_tz":360,"elapsed":2361,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"02a45268-f053-4947-ac73-9a52b7569a42","colab":{"base_uri":"https://localhost:8080/"}},"source":["def fold_k_err(X,y,k,G):\n","    np.random.seed(1)\n","    fold = np.random.choice(np.arange(5), len(y))\n","    Xtrain, ytrain = X[fold != k, :], y[fold != k]\n","    Xtest, ytest = X[fold == k, :], y[fold == k]\n","    ng = np.asarray([sum(ytrain==i) for i in np.arange(10)])\n","    n = np.hstack((ng.reshape((-1,1)), np.tile([110,90,65, 60,55,50],\n","                                 10).reshape((10,-1))))\n","    p = np.array([8,10, 12,15,17,56]) \n","    return compute_err(Xtrain, ytrain, Xtest, ytest, n, p, G)\n","# cross_validation error\n","res = [fold_k_err(X,y,k,10) for k in np.arange(5)]\n","res50 = np.mean(np.asarray(res), axis=0)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[SoftImpute] Max Singular Value of X_init = 80.448772\n","[SoftImpute] Iter 1: observed MAE=0.041334 rank=49\n","[SoftImpute] Iter 2: observed MAE=0.041441 rank=49\n","[SoftImpute] Iter 3: observed MAE=0.041538 rank=49\n","[SoftImpute] Iter 4: observed MAE=0.041614 rank=49\n","[SoftImpute] Iter 5: observed MAE=0.041675 rank=49\n","[SoftImpute] Iter 6: observed MAE=0.041724 rank=49\n","[SoftImpute] Iter 7: observed MAE=0.041765 rank=49\n","[SoftImpute] Iter 8: observed MAE=0.041800 rank=49\n","[SoftImpute] Iter 9: observed MAE=0.041829 rank=49\n","[SoftImpute] Iter 10: observed MAE=0.041854 rank=49\n","[SoftImpute] Iter 11: observed MAE=0.041877 rank=49\n","[SoftImpute] Iter 12: observed MAE=0.041896 rank=49\n","[SoftImpute] Iter 13: observed MAE=0.041913 rank=49\n","[SoftImpute] Iter 14: observed MAE=0.041928 rank=49\n","[SoftImpute] Iter 15: observed MAE=0.041941 rank=49\n","[SoftImpute] Iter 16: observed MAE=0.041953 rank=49\n","[SoftImpute] Iter 17: observed MAE=0.041964 rank=49\n","[SoftImpute] Iter 18: observed 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Iter 54: observed MAE=0.042074 rank=49\n","[SoftImpute] Iter 55: observed MAE=0.042074 rank=49\n","[SoftImpute] Iter 56: observed MAE=0.042075 rank=49\n","[SoftImpute] Iter 57: observed MAE=0.042076 rank=49\n","[SoftImpute] Iter 58: observed MAE=0.042076 rank=49\n","[SoftImpute] Iter 59: observed MAE=0.042077 rank=49\n","[SoftImpute] Iter 60: observed MAE=0.042077 rank=49\n","[SoftImpute] Iter 61: observed MAE=0.042078 rank=49\n","[SoftImpute] Iter 62: observed MAE=0.042078 rank=49\n","[SoftImpute] Iter 63: observed MAE=0.042079 rank=49\n","[SoftImpute] Iter 64: observed MAE=0.042079 rank=49\n","[SoftImpute] Iter 65: observed MAE=0.042080 rank=49\n","[SoftImpute] Iter 66: observed MAE=0.042080 rank=49\n","[SoftImpute] Iter 67: observed MAE=0.042080 rank=49\n","[SoftImpute] Iter 68: observed MAE=0.042081 rank=49\n","[SoftImpute] Iter 69: observed MAE=0.042081 rank=49\n","[SoftImpute] Iter 70: observed MAE=0.042082 rank=49\n","[SoftImpute] Iter 71: observed MAE=0.042082 rank=49\n","[SoftImpute] Iter 72: observed MAE=0.042082 rank=49\n","[SoftImpute] Iter 73: observed MAE=0.042083 rank=49\n","[SoftImpute] Iter 74: observed MAE=0.042083 rank=49\n","[SoftImpute] Iter 75: observed MAE=0.042083 rank=49\n","[SoftImpute] Iter 76: observed MAE=0.042084 rank=49\n","[SoftImpute] Iter 77: observed MAE=0.042084 rank=49\n","[SoftImpute] Iter 78: observed MAE=0.042084 rank=49\n","[SoftImpute] Iter 79: observed MAE=0.042085 rank=49\n","[SoftImpute] Iter 80: observed MAE=0.042085 rank=49\n","[SoftImpute] Iter 81: observed MAE=0.042085 rank=49\n","[SoftImpute] Iter 82: observed MAE=0.042086 rank=49\n","[SoftImpute] Iter 83: observed MAE=0.042086 rank=49\n","[SoftImpute] Iter 84: observed MAE=0.042086 rank=49\n","[SoftImpute] Iter 85: observed MAE=0.042086 rank=49\n","[SoftImpute] Iter 86: observed MAE=0.042087 rank=49\n","[SoftImpute] Iter 87: observed MAE=0.042087 rank=49\n","[SoftImpute] Iter 88: observed MAE=0.042087 rank=49\n","[SoftImpute] Iter 89: observed MAE=0.042088 rank=49\n","[SoftImpute] Iter 90: observed MAE=0.042088 rank=49\n","[SoftImpute] Iter 91: observed MAE=0.042088 rank=49\n","[SoftImpute] Iter 92: observed MAE=0.042088 rank=49\n","[SoftImpute] Iter 93: observed MAE=0.042089 rank=49\n","[SoftImpute] Iter 94: observed MAE=0.042089 rank=49\n","[SoftImpute] Iter 95: observed MAE=0.042089 rank=49\n","[SoftImpute] Iter 96: observed MAE=0.042089 rank=49\n","[SoftImpute] Iter 97: observed MAE=0.042090 rank=49\n","[SoftImpute] Iter 98: observed MAE=0.042090 rank=49\n","[SoftImpute] Iter 99: observed MAE=0.042090 rank=49\n","[SoftImpute] Iter 100: observed MAE=0.042090 rank=49\n","[SoftImpute] Stopped after iteration 100 for lambda=1.608975\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 1571166\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 1261092, constraints m = 1415856\n","Cones:\tprimal zero / dual free vars: 77382\n","\tlinear vars: 232146\n","\tsd vars: 1106328, sd blks: 1\n","Setup time: 2.35e+00s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.52e+22  1.49e+22  1.00e+00 -3.21e+25  5.97e+24  7.76e+24  1.99e+00 \n","   100| 1.24e-03  1.52e-03  1.85e-04  4.21e+02  4.21e+02  1.35e-14  5.34e+02 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 5.34e+02s\n","\tLin-sys: nnz in L factor: 4287078, avg solve time: 4.04e-02s\n","\tCones: avg projection time: 4.77e+00s\n","\tAcceleration: avg step time: 3.90e-01s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 1.8444e-09, dist(y, K*) = 6.0992e-09, s'y/|s||y| = -1.7055e-13\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.6278e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.7506e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.9703e-04\n","----------------------------------------------------------------------------\n","c'x = 420.7028, -b'y = 420.8688\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 80.925386\n","[SoftImpute] Iter 1: observed MAE=0.041056 rank=49\n","[SoftImpute] Iter 2: observed MAE=0.041150 rank=49\n","[SoftImpute] Iter 3: observed MAE=0.041235 rank=49\n","[SoftImpute] Iter 4: observed MAE=0.041306 rank=49\n","[SoftImpute] Iter 5: observed MAE=0.041365 rank=49\n","[SoftImpute] Iter 6: observed MAE=0.041413 rank=49\n","[SoftImpute] Iter 7: observed MAE=0.041453 rank=49\n","[SoftImpute] Iter 8: observed MAE=0.041486 rank=48\n","[SoftImpute] Iter 9: observed MAE=0.041513 rank=48\n","[SoftImpute] Iter 10: observed MAE=0.041537 rank=48\n","[SoftImpute] Iter 11: observed MAE=0.041558 rank=48\n","[SoftImpute] Iter 12: observed MAE=0.041577 rank=48\n","[SoftImpute] Iter 13: observed MAE=0.041593 rank=48\n","[SoftImpute] Iter 14: observed MAE=0.041608 rank=48\n","[SoftImpute] Iter 15: observed MAE=0.041621 rank=48\n","[SoftImpute] Iter 16: observed MAE=0.041633 rank=48\n","[SoftImpute] Iter 17: observed MAE=0.041643 rank=48\n","[SoftImpute] Iter 18: observed MAE=0.041653 rank=48\n","[SoftImpute] Iter 19: observed MAE=0.041661 rank=48\n","[SoftImpute] Iter 20: observed MAE=0.041669 rank=48\n","[SoftImpute] Iter 21: observed MAE=0.041676 rank=48\n","[SoftImpute] Iter 22: observed MAE=0.041683 rank=48\n","[SoftImpute] Iter 23: observed 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rank=48\n","[SoftImpute] Iter 77: observed MAE=0.041769 rank=48\n","[SoftImpute] Iter 78: observed MAE=0.041770 rank=48\n","[SoftImpute] Iter 79: observed MAE=0.041770 rank=48\n","[SoftImpute] Iter 80: observed MAE=0.041770 rank=48\n","[SoftImpute] Iter 81: observed MAE=0.041771 rank=48\n","[SoftImpute] Iter 82: observed MAE=0.041771 rank=48\n","[SoftImpute] Iter 83: observed MAE=0.041771 rank=48\n","[SoftImpute] Iter 84: observed MAE=0.041772 rank=48\n","[SoftImpute] Iter 85: observed MAE=0.041772 rank=48\n","[SoftImpute] Iter 86: observed MAE=0.041772 rank=48\n","[SoftImpute] Iter 87: observed MAE=0.041773 rank=48\n","[SoftImpute] Iter 88: observed MAE=0.041773 rank=48\n","[SoftImpute] Iter 89: observed MAE=0.041773 rank=48\n","[SoftImpute] Iter 90: observed MAE=0.041774 rank=48\n","[SoftImpute] Iter 91: observed MAE=0.041774 rank=48\n","[SoftImpute] Iter 92: observed MAE=0.041774 rank=48\n","[SoftImpute] Iter 93: observed MAE=0.041774 rank=48\n","[SoftImpute] Iter 94: observed MAE=0.041775 rank=48\n","[SoftImpute] Iter 95: observed MAE=0.041775 rank=48\n","[SoftImpute] Iter 96: observed MAE=0.041775 rank=48\n","[SoftImpute] Iter 97: observed MAE=0.041776 rank=48\n","[SoftImpute] Iter 98: observed MAE=0.041776 rank=48\n","[SoftImpute] Iter 99: observed MAE=0.041776 rank=48\n","[SoftImpute] Iter 100: observed MAE=0.041776 rank=48\n","[SoftImpute] Stopped after iteration 100 for lambda=1.618508\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 1615816\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 1301292, constraints m = 1458756\n","Cones:\tprimal zero / dual free vars: 78732\n","\tlinear vars: 236196\n","\tsd vars: 1143828, sd blks: 1\n","Setup time: 1.54e+00s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.54e+22  1.52e+22  1.00e+00 -3.30e+25  6.13e+24  7.94e+24  2.05e+00 \n","   100| 8.10e-04  1.24e-03  3.33e-04  4.18e+02  4.17e+02  7.69e-14  5.06e+02 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 5.06e+02s\n","\tLin-sys: nnz in L factor: 4415028, avg solve time: 4.11e-02s\n","\tCones: avg projection time: 4.48e+00s\n","\tAcceleration: avg step time: 3.98e-01s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.7744e-09, dist(y, K*) = 1.0520e-08, s'y/|s||y| = -4.8890e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.3287e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.7823e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 5.1380e-05\n","----------------------------------------------------------------------------\n","c'x = 418.0096, -b'y = 418.0526\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 80.369800\n","[SoftImpute] Iter 1: observed MAE=0.041293 rank=49\n","[SoftImpute] Iter 2: observed MAE=0.041375 rank=49\n","[SoftImpute] Iter 3: observed MAE=0.041459 rank=49\n","[SoftImpute] Iter 4: observed MAE=0.041530 rank=49\n","[SoftImpute] Iter 5: observed MAE=0.041588 rank=49\n","[SoftImpute] Iter 6: observed MAE=0.041636 rank=49\n","[SoftImpute] Iter 7: observed MAE=0.041676 rank=49\n","[SoftImpute] Iter 8: observed MAE=0.041709 rank=49\n","[SoftImpute] Iter 9: observed MAE=0.041737 rank=49\n","[SoftImpute] Iter 10: observed MAE=0.041761 rank=49\n","[SoftImpute] Iter 11: observed MAE=0.041783 rank=49\n","[SoftImpute] Iter 12: observed MAE=0.041801 rank=49\n","[SoftImpute] Iter 13: observed MAE=0.041818 rank=49\n","[SoftImpute] Iter 14: observed MAE=0.041833 rank=49\n","[SoftImpute] Iter 15: observed MAE=0.041846 rank=49\n","[SoftImpute] Iter 16: observed MAE=0.041858 rank=49\n","[SoftImpute] Iter 17: observed MAE=0.041869 rank=49\n","[SoftImpute] Iter 18: observed MAE=0.041879 rank=49\n","[SoftImpute] Iter 19: observed MAE=0.041888 rank=49\n","[SoftImpute] Iter 20: observed MAE=0.041896 rank=49\n","[SoftImpute] Iter 21: observed MAE=0.041903 rank=49\n","[SoftImpute] Iter 22: observed MAE=0.041910 rank=49\n","[SoftImpute] Iter 23: observed MAE=0.041917 rank=49\n","[SoftImpute] Iter 24: observed MAE=0.041923 rank=49\n","[SoftImpute] Iter 25: observed MAE=0.041928 rank=49\n","[SoftImpute] Iter 26: observed MAE=0.041933 rank=49\n","[SoftImpute] Iter 27: observed MAE=0.041938 rank=49\n","[SoftImpute] Iter 28: observed MAE=0.041942 rank=49\n","[SoftImpute] Iter 29: observed MAE=0.041946 rank=49\n","[SoftImpute] Iter 30: observed MAE=0.041949 rank=49\n","[SoftImpute] Iter 31: observed MAE=0.041952 rank=49\n","[SoftImpute] Iter 32: observed MAE=0.041955 rank=49\n","[SoftImpute] Iter 33: observed MAE=0.041958 rank=49\n","[SoftImpute] Iter 34: observed MAE=0.041960 rank=49\n","[SoftImpute] Iter 35: observed MAE=0.041963 rank=49\n","[SoftImpute] Iter 36: observed MAE=0.041965 rank=49\n","[SoftImpute] Iter 37: observed MAE=0.041967 rank=49\n","[SoftImpute] Iter 38: observed MAE=0.041969 rank=49\n","[SoftImpute] Iter 39: observed MAE=0.041970 rank=49\n","[SoftImpute] Iter 40: observed MAE=0.041972 rank=49\n","[SoftImpute] Iter 41: observed MAE=0.041974 rank=49\n","[SoftImpute] Iter 42: observed MAE=0.041975 rank=49\n","[SoftImpute] Iter 43: observed MAE=0.041976 rank=49\n","[SoftImpute] Iter 44: observed MAE=0.041978 rank=49\n","[SoftImpute] Iter 45: observed MAE=0.041979 rank=49\n","[SoftImpute] Iter 46: observed MAE=0.041980 rank=49\n","[SoftImpute] Iter 47: observed MAE=0.041981 rank=49\n","[SoftImpute] Iter 48: observed MAE=0.041982 rank=49\n","[SoftImpute] Iter 49: observed MAE=0.041983 rank=49\n","[SoftImpute] Iter 50: observed MAE=0.041984 rank=49\n","[SoftImpute] Iter 51: observed MAE=0.041985 rank=49\n","[SoftImpute] Iter 52: observed MAE=0.041986 rank=49\n","[SoftImpute] Iter 53: observed MAE=0.041987 rank=49\n","[SoftImpute] Iter 54: observed MAE=0.041987 rank=49\n","[SoftImpute] Iter 55: observed MAE=0.041988 rank=49\n","[SoftImpute] Iter 56: observed MAE=0.041989 rank=49\n","[SoftImpute] Iter 57: observed MAE=0.041989 rank=49\n","[SoftImpute] Iter 58: observed MAE=0.041990 rank=49\n","[SoftImpute] Iter 59: observed MAE=0.041991 rank=49\n","[SoftImpute] Iter 60: observed MAE=0.041991 rank=49\n","[SoftImpute] Iter 61: observed MAE=0.041992 rank=49\n","[SoftImpute] Iter 62: observed MAE=0.041992 rank=49\n","[SoftImpute] Iter 63: observed MAE=0.041993 rank=49\n","[SoftImpute] 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rank=49\n","[SoftImpute] Iter 82: observed MAE=0.042001 rank=49\n","[SoftImpute] Iter 83: observed MAE=0.042001 rank=49\n","[SoftImpute] Iter 84: observed MAE=0.042001 rank=49\n","[SoftImpute] Iter 85: observed MAE=0.042002 rank=49\n","[SoftImpute] Iter 86: observed MAE=0.042002 rank=49\n","[SoftImpute] Iter 87: observed MAE=0.042002 rank=49\n","[SoftImpute] Iter 88: observed MAE=0.042002 rank=49\n","[SoftImpute] Iter 89: observed MAE=0.042003 rank=49\n","[SoftImpute] Iter 90: observed MAE=0.042003 rank=49\n","[SoftImpute] Iter 91: observed MAE=0.042003 rank=49\n","[SoftImpute] Iter 92: observed MAE=0.042004 rank=49\n","[SoftImpute] Iter 93: observed MAE=0.042004 rank=49\n","[SoftImpute] Iter 94: observed MAE=0.042004 rank=49\n","[SoftImpute] Iter 95: observed MAE=0.042004 rank=49\n","[SoftImpute] Iter 96: observed MAE=0.042005 rank=49\n","[SoftImpute] Iter 97: observed MAE=0.042005 rank=49\n","[SoftImpute] Iter 98: observed MAE=0.042005 rank=49\n","[SoftImpute] Iter 99: observed MAE=0.042006 rank=49\n","[SoftImpute] Iter 100: observed MAE=0.042006 rank=49\n","[SoftImpute] Stopped after iteration 100 for lambda=1.607396\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 1551718\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 1243602, constraints m = 1397178\n","Cones:\tprimal zero / dual free vars: 76788\n","\tlinear vars: 230364\n","\tsd vars: 1090026, sd blks: 1\n","Setup time: 1.43e+00s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.50e+22  1.48e+22  1.00e+00 -3.17e+25  5.90e+24  7.69e+24  1.87e+00 \n","   100| 1.43e-03  2.02e-03  1.67e-05  4.20e+02  4.20e+02  3.57e-13  4.84e+02 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 4.84e+02s\n","\tLin-sys: nnz in L factor: 4231374, avg solve time: 4.05e-02s\n","\tCones: avg projection time: 4.27e+00s\n","\tAcceleration: avg step time: 3.84e-01s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 6.8302e-09, dist(y, K*) = 1.5529e-08, s'y/|s||y| = 5.0000e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 2.8341e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.3306e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.5483e-04\n","----------------------------------------------------------------------------\n","c'x = 420.0479, -b'y = 419.9177\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 80.787214\n","[SoftImpute] Iter 1: observed MAE=0.041269 rank=49\n","[SoftImpute] Iter 2: observed MAE=0.041354 rank=49\n","[SoftImpute] Iter 3: observed MAE=0.041439 rank=49\n","[SoftImpute] Iter 4: observed MAE=0.041511 rank=49\n","[SoftImpute] Iter 5: observed MAE=0.041568 rank=49\n","[SoftImpute] Iter 6: observed MAE=0.041615 rank=49\n","[SoftImpute] Iter 7: observed MAE=0.041655 rank=49\n","[SoftImpute] Iter 8: observed MAE=0.041689 rank=49\n","[SoftImpute] Iter 9: observed MAE=0.041718 rank=49\n","[SoftImpute] Iter 10: observed MAE=0.041742 rank=49\n","[SoftImpute] Iter 11: observed MAE=0.041764 rank=49\n","[SoftImpute] Iter 12: observed MAE=0.041783 rank=49\n","[SoftImpute] Iter 13: observed MAE=0.041800 rank=49\n","[SoftImpute] Iter 14: observed MAE=0.041815 rank=49\n","[SoftImpute] Iter 15: observed MAE=0.041828 rank=49\n","[SoftImpute] Iter 16: observed MAE=0.041841 rank=49\n","[SoftImpute] Iter 17: observed MAE=0.041852 rank=49\n","[SoftImpute] Iter 18: observed MAE=0.041862 rank=49\n","[SoftImpute] Iter 19: observed MAE=0.041872 rank=49\n","[SoftImpute] Iter 20: observed MAE=0.041880 rank=49\n","[SoftImpute] Iter 21: observed MAE=0.041888 rank=49\n","[SoftImpute] Iter 22: observed MAE=0.041895 rank=49\n","[SoftImpute] Iter 23: observed MAE=0.041901 rank=49\n","[SoftImpute] Iter 24: observed MAE=0.041907 rank=49\n","[SoftImpute] Iter 25: observed MAE=0.041912 rank=49\n","[SoftImpute] Iter 26: observed MAE=0.041917 rank=49\n","[SoftImpute] Iter 27: observed MAE=0.041921 rank=49\n","[SoftImpute] Iter 28: observed MAE=0.041925 rank=49\n","[SoftImpute] Iter 29: observed MAE=0.041929 rank=49\n","[SoftImpute] Iter 30: observed MAE=0.041933 rank=49\n","[SoftImpute] Iter 31: observed 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observed MAE=0.041970 rank=49\n","[SoftImpute] Iter 50: observed MAE=0.041971 rank=49\n","[SoftImpute] Iter 51: observed MAE=0.041972 rank=49\n","[SoftImpute] Iter 52: observed MAE=0.041973 rank=49\n","[SoftImpute] Iter 53: observed MAE=0.041974 rank=49\n","[SoftImpute] Iter 54: observed MAE=0.041974 rank=49\n","[SoftImpute] Iter 55: observed MAE=0.041975 rank=49\n","[SoftImpute] Iter 56: observed MAE=0.041976 rank=49\n","[SoftImpute] Iter 57: observed MAE=0.041977 rank=49\n","[SoftImpute] Iter 58: observed MAE=0.041978 rank=49\n","[SoftImpute] Iter 59: observed MAE=0.041978 rank=49\n","[SoftImpute] Iter 60: observed MAE=0.041979 rank=49\n","[SoftImpute] Iter 61: observed MAE=0.041980 rank=49\n","[SoftImpute] Iter 62: observed MAE=0.041980 rank=49\n","[SoftImpute] Iter 63: observed MAE=0.041981 rank=49\n","[SoftImpute] Iter 64: observed MAE=0.041982 rank=49\n","[SoftImpute] Iter 65: observed MAE=0.041982 rank=49\n","[SoftImpute] Iter 66: observed MAE=0.041983 rank=49\n","[SoftImpute] Iter 67: observed MAE=0.041983 rank=49\n","[SoftImpute] Iter 68: observed MAE=0.041984 rank=49\n","[SoftImpute] Iter 69: observed MAE=0.041984 rank=49\n","[SoftImpute] Iter 70: observed MAE=0.041985 rank=49\n","[SoftImpute] Iter 71: observed MAE=0.041985 rank=49\n","[SoftImpute] Iter 72: observed MAE=0.041986 rank=49\n","[SoftImpute] Iter 73: observed MAE=0.041986 rank=49\n","[SoftImpute] Iter 74: observed MAE=0.041987 rank=49\n","[SoftImpute] Iter 75: observed MAE=0.041987 rank=49\n","[SoftImpute] Iter 76: observed MAE=0.041988 rank=49\n","[SoftImpute] Iter 77: observed MAE=0.041988 rank=49\n","[SoftImpute] Iter 78: observed MAE=0.041988 rank=49\n","[SoftImpute] Iter 79: observed MAE=0.041989 rank=49\n","[SoftImpute] Iter 80: observed MAE=0.041989 rank=49\n","[SoftImpute] Iter 81: observed MAE=0.041990 rank=49\n","[SoftImpute] Iter 82: observed MAE=0.041990 rank=49\n","[SoftImpute] Iter 83: observed MAE=0.041990 rank=49\n","[SoftImpute] Iter 84: observed MAE=0.041991 rank=49\n","[SoftImpute] Iter 85: observed MAE=0.041991 rank=49\n","[SoftImpute] Iter 86: observed MAE=0.041991 rank=49\n","[SoftImpute] Iter 87: observed MAE=0.041992 rank=49\n","[SoftImpute] Iter 88: observed MAE=0.041992 rank=49\n","[SoftImpute] Iter 89: observed MAE=0.041992 rank=49\n","[SoftImpute] Iter 90: observed MAE=0.041993 rank=49\n","[SoftImpute] Iter 91: observed MAE=0.041993 rank=49\n","[SoftImpute] Iter 92: observed MAE=0.041993 rank=49\n","[SoftImpute] Iter 93: observed MAE=0.041994 rank=49\n","[SoftImpute] Iter 94: observed MAE=0.041994 rank=49\n","[SoftImpute] Iter 95: observed MAE=0.041994 rank=49\n","[SoftImpute] Iter 96: observed MAE=0.041995 rank=49\n","[SoftImpute] Iter 97: observed MAE=0.041995 rank=49\n","[SoftImpute] Iter 98: observed MAE=0.041995 rank=49\n","[SoftImpute] Iter 99: observed MAE=0.041996 rank=49\n","[SoftImpute] Iter 100: observed MAE=0.041996 rank=49\n","[SoftImpute] Stopped after iteration 100 for lambda=1.615744\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 1583605\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 1272285, constraints m = 1427805\n","Cones:\tprimal zero / dual free vars: 77760\n","\tlinear vars: 233280\n","\tsd vars: 1116765, sd blks: 1\n","Setup time: 1.48e+00s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.52e+22  1.50e+22  1.00e+00 -3.23e+25  6.01e+24  7.81e+24  2.06e+00 \n","   100| 9.13e-04  8.63e-04  4.66e-04  4.19e+02  4.19e+02  1.97e-13  5.38e+02 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 5.38e+02s\n","\tLin-sys: nnz in L factor: 4322715, avg solve time: 4.09e-02s\n","\tCones: avg projection time: 4.80e+00s\n","\tAcceleration: avg step time: 3.95e-01s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 2.5023e-09, dist(y, K*) = 2.2883e-08, s'y/|s||y| = -5.6217e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.6365e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 4.4230e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.1193e-04\n","----------------------------------------------------------------------------\n","c'x = 418.7618, -b'y = 418.6680\n","============================================================================\n","[SoftImpute] Max Singular Value of X_init = 80.722492\n","[SoftImpute] Iter 1: observed MAE=0.041341 rank=49\n","[SoftImpute] Iter 2: observed MAE=0.041425 rank=49\n","[SoftImpute] Iter 3: observed MAE=0.041512 rank=49\n","[SoftImpute] Iter 4: observed MAE=0.041586 rank=49\n","[SoftImpute] Iter 5: observed MAE=0.041647 rank=49\n","[SoftImpute] Iter 6: observed MAE=0.041697 rank=49\n","[SoftImpute] Iter 7: observed MAE=0.041738 rank=49\n","[SoftImpute] Iter 8: observed MAE=0.041773 rank=49\n","[SoftImpute] Iter 9: observed MAE=0.041802 rank=49\n","[SoftImpute] Iter 10: observed MAE=0.041828 rank=49\n","[SoftImpute] Iter 11: observed MAE=0.041850 rank=49\n","[SoftImpute] Iter 12: observed MAE=0.041869 rank=49\n","[SoftImpute] Iter 13: observed MAE=0.041886 rank=49\n","[SoftImpute] Iter 14: observed MAE=0.041901 rank=49\n","[SoftImpute] Iter 15: observed MAE=0.041915 rank=49\n","[SoftImpute] Iter 16: observed MAE=0.041927 rank=49\n","[SoftImpute] Iter 17: observed MAE=0.041938 rank=49\n","[SoftImpute] Iter 18: observed MAE=0.041948 rank=49\n","[SoftImpute] Iter 19: observed MAE=0.041957 rank=49\n","[SoftImpute] Iter 20: observed MAE=0.041965 rank=49\n","[SoftImpute] Iter 21: observed MAE=0.041973 rank=49\n","[SoftImpute] Iter 22: observed MAE=0.041980 rank=49\n","[SoftImpute] Iter 23: observed MAE=0.041986 rank=49\n","[SoftImpute] Iter 24: observed MAE=0.041991 rank=49\n","[SoftImpute] Iter 25: observed MAE=0.041997 rank=49\n","[SoftImpute] Iter 26: observed MAE=0.042001 rank=49\n","[SoftImpute] Iter 27: observed MAE=0.042006 rank=49\n","[SoftImpute] Iter 28: observed MAE=0.042009 rank=49\n","[SoftImpute] Iter 29: observed MAE=0.042013 rank=49\n","[SoftImpute] Iter 30: observed MAE=0.042016 rank=49\n","[SoftImpute] Iter 31: observed MAE=0.042019 rank=49\n","[SoftImpute] Iter 32: observed MAE=0.042022 rank=49\n","[SoftImpute] Iter 33: observed MAE=0.042025 rank=49\n","[SoftImpute] Iter 34: observed MAE=0.042027 rank=49\n","[SoftImpute] Iter 35: observed MAE=0.042030 rank=49\n","[SoftImpute] Iter 36: observed MAE=0.042032 rank=49\n","[SoftImpute] Iter 37: observed MAE=0.042034 rank=49\n","[SoftImpute] Iter 38: observed MAE=0.042035 rank=49\n","[SoftImpute] Iter 39: observed MAE=0.042037 rank=49\n","[SoftImpute] Iter 40: observed MAE=0.042039 rank=49\n","[SoftImpute] Iter 41: observed MAE=0.042040 rank=49\n","[SoftImpute] Iter 42: observed MAE=0.042042 rank=49\n","[SoftImpute] Iter 43: observed MAE=0.042043 rank=49\n","[SoftImpute] Iter 44: observed MAE=0.042044 rank=49\n","[SoftImpute] Iter 45: observed MAE=0.042046 rank=49\n","[SoftImpute] Iter 46: observed MAE=0.042047 rank=49\n","[SoftImpute] Iter 47: observed MAE=0.042048 rank=49\n","[SoftImpute] Iter 48: observed MAE=0.042049 rank=49\n","[SoftImpute] Iter 49: observed MAE=0.042050 rank=49\n","[SoftImpute] Iter 50: observed MAE=0.042051 rank=49\n","[SoftImpute] Iter 51: observed MAE=0.042051 rank=49\n","[SoftImpute] Iter 52: observed MAE=0.042052 rank=49\n","[SoftImpute] Iter 53: observed MAE=0.042053 rank=49\n","[SoftImpute] Iter 54: observed MAE=0.042054 rank=49\n","[SoftImpute] Iter 55: observed MAE=0.042055 rank=49\n","[SoftImpute] Iter 56: observed MAE=0.042055 rank=49\n","[SoftImpute] Iter 57: observed MAE=0.042056 rank=49\n","[SoftImpute] Iter 58: observed MAE=0.042057 rank=49\n","[SoftImpute] Iter 59: observed MAE=0.042057 rank=49\n","[SoftImpute] Iter 60: observed MAE=0.042058 rank=49\n","[SoftImpute] Iter 61: observed MAE=0.042058 rank=49\n","[SoftImpute] Iter 62: observed MAE=0.042059 rank=49\n","[SoftImpute] Iter 63: observed MAE=0.042059 rank=49\n","[SoftImpute] Iter 64: observed MAE=0.042060 rank=49\n","[SoftImpute] Iter 65: observed MAE=0.042060 rank=49\n","[SoftImpute] Iter 66: observed MAE=0.042061 rank=49\n","[SoftImpute] Iter 67: observed MAE=0.042061 rank=49\n","[SoftImpute] Iter 68: observed MAE=0.042062 rank=49\n","[SoftImpute] Iter 69: observed MAE=0.042062 rank=49\n","[SoftImpute] Iter 70: observed MAE=0.042062 rank=49\n","[SoftImpute] Iter 71: observed MAE=0.042063 rank=49\n","[SoftImpute] Iter 72: observed MAE=0.042063 rank=49\n","[SoftImpute] Iter 73: observed MAE=0.042064 rank=49\n","[SoftImpute] Iter 74: observed MAE=0.042064 rank=49\n","[SoftImpute] Iter 75: observed MAE=0.042064 rank=49\n","[SoftImpute] Iter 76: observed MAE=0.042065 rank=49\n","[SoftImpute] Iter 77: observed MAE=0.042065 rank=49\n","[SoftImpute] Iter 78: observed MAE=0.042065 rank=49\n","[SoftImpute] Iter 79: observed MAE=0.042066 rank=49\n","[SoftImpute] Iter 80: observed MAE=0.042066 rank=49\n","[SoftImpute] Iter 81: observed MAE=0.042066 rank=49\n","[SoftImpute] Iter 82: observed MAE=0.042067 rank=49\n","[SoftImpute] Iter 83: observed MAE=0.042067 rank=49\n","[SoftImpute] Iter 84: observed MAE=0.042067 rank=49\n","[SoftImpute] Iter 85: observed MAE=0.042068 rank=49\n","[SoftImpute] Iter 86: observed MAE=0.042068 rank=49\n","[SoftImpute] Iter 87: observed MAE=0.042068 rank=49\n","[SoftImpute] Iter 88: observed MAE=0.042069 rank=49\n","[SoftImpute] Iter 89: observed MAE=0.042069 rank=49\n","[SoftImpute] Iter 90: observed MAE=0.042069 rank=49\n","[SoftImpute] Iter 91: observed MAE=0.042069 rank=49\n","[SoftImpute] Iter 92: observed MAE=0.042070 rank=49\n","[SoftImpute] Iter 93: observed MAE=0.042070 rank=49\n","[SoftImpute] Iter 94: observed MAE=0.042070 rank=49\n","[SoftImpute] Iter 95: observed MAE=0.042070 rank=49\n","[SoftImpute] Iter 96: observed MAE=0.042071 rank=49\n","[SoftImpute] Iter 97: observed MAE=0.042071 rank=49\n","[SoftImpute] Iter 98: observed MAE=0.042071 rank=49\n","[SoftImpute] Iter 99: observed MAE=0.042071 rank=49\n","[SoftImpute] Iter 100: observed MAE=0.042071 rank=49\n","[SoftImpute] Stopped after iteration 100 for lambda=1.614450\n","----------------------------------------------------------------------------\n","\tSCS v2.1.2 - Splitting Conic Solver\n","\t(c) Brendan O'Donoghue, Stanford University, 2012\n","----------------------------------------------------------------------------\n","Lin-sys: sparse-direct, nnz in A = 1574715\n","eps = 1.00e-04, alpha = 1.50, max_iters = 100, normalize = 1, scale = 1.00\n","acceleration_lookback = 10, rho_x = 1.00e-03\n","Variables n = 1264285, constraints m = 1419265\n","Cones:\tprimal zero / dual free vars: 77490\n","\tlinear vars: 232470\n","\tsd vars: 1109305, sd blks: 1\n","Setup time: 1.53e+00s\n","----------------------------------------------------------------------------\n"," Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n","----------------------------------------------------------------------------\n","     0| 1.52e+22  1.49e+22  1.00e+00 -3.22e+25  5.98e+24  7.77e+24  2.07e+00 \n","   100| 7.19e-04  7.12e-04  8.36e-05  4.18e+02  4.18e+02  3.01e-13  5.31e+02 \n","----------------------------------------------------------------------------\n","Status: Solved/Inaccurate\n","Hit max_iters, solution may be inaccurate, returning best found solution.\n","Timing: Solve time: 5.31e+02s\n","\tLin-sys: nnz in L factor: 4297245, avg solve time: 4.08e-02s\n","\tCones: avg projection time: 4.73e+00s\n","\tAcceleration: avg step time: 3.95e-01s\n","----------------------------------------------------------------------------\n","Error metrics:\n","dist(s, K) = 5.6521e-09, dist(y, K*) = 9.8214e-09, s'y/|s||y| = 1.1448e-14\n","primal res: |Ax + s - b|_2 / (1 + |b|_2) = 3.4262e-04\n","dual res:   |A'y + c|_2 / (1 + |c|_2) = 3.8114e-04\n","rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 6.4591e-04\n","----------------------------------------------------------------------------\n","c'x = 417.7020, -b'y = 417.1621\n","============================================================================\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"inTfAg4MIIPb","executionInfo":{"status":"ok","timestamp":1604561966411,"user_tz":360,"elapsed":40,"user":{"displayName":"Thu Nguyễn","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjaRl8WgKOjLdrEa69IqFm__Rq7udZ763hhFDl9=s64","userId":"04714273295929622355"}},"outputId":"de141a63-951c-42e2-e397-457091c12124","colab":{"base_uri":"https://localhost:8080/"}},"source":["res50"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0.07666361, 0.09432159, 0.08668356, 0.09460065, 0.14421478,\n","       0.09679918, 0.49758553])"]},"metadata":{"tags":[]},"execution_count":118}]},{"cell_type":"code","metadata":{"id":"vA4tWPcFIJVU"},"source":[""],"execution_count":null,"outputs":[]}]}