learnCurve.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12L, 1L) (21L, 1L) (21L, 1L)\n"
     ]
    },
    {
     "data": {
      "image/png": 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nfj6wN4CySYD+A3hxROwFjAPH5Yj73rT9IuA9VdZfATxf0jPIRj1PxP184HLg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\n+tz/AtOZvwUT+mnLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5f3f978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#本文是绘制学习曲线，学会误差分析,从而进行模型诊断和选择\n",
    "#Loading and Visualizing Data\n",
    "import numpy as np\n",
    "import scipy.io as sio\n",
    "import matplotlib.pyplot as plt\n",
    "data = sio.loadmat('ex5data1.mat')\n",
    "X = data['X']\n",
    "y = data['y']\n",
    "Xval = data['Xval']\n",
    "yval = data['yval']\n",
    "Xtest = data['Xtest']\n",
    "ytest = data['ytest']\n",
    "print X.shape,Xval.shape,Xtest.shape\n",
    "\n",
    "plt.plot(X,y,'rx',markersize= 10,linewidth= 1.5)\n",
    "plt.xlabel('Change in water level (x)')\n",
    "plt.ylabel('Water flowing out of the dam (y)')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at theta = [1 ; 1]: (this value should be about 303.993192)\n303.99319222\nGradient at theta = [1 ; 1](this value should be about [-15.303016; 598.250744])\n[[ -15.30301567]\n [ 598.25074417]]\n"
     ]
    }
   ],
   "source": [
    "#正则化用于线性回归\n",
    "def linearRegCostFunction(X,y,theta,reg):\n",
    "    m,n = X.shape\n",
    "    J = 0\n",
    "    theta = theta.reshape((n,1))\n",
    "    grad = np.zeros_like(theta)\n",
    "    theta1 = theta[1:,:]\n",
    "    J = 0.5 * np.sum((X.dot(theta)-y)**2) / m + reg * 0.5 * np.sum(theta1**2) / m\n",
    "    grad = X.T.dot(X.dot(theta) - y) / m\n",
    "    grad[1:,:] += reg * theta1 / m  #float reg = 1--->reg = 1.0\n",
    "    return J,grad\n",
    "\n",
    "m = X.shape[0]\n",
    "XX = np.hstack((np.ones((m,1)),X))  #add the x0 = 1\n",
    "XXval = np.hstack((np.ones((Xval.shape[0],1)),Xval))\n",
    "XXtest = np.hstack((np.ones((Xtest.shape[0],1)),Xtest)) \n",
    "#还是用简单的数测试一下正确性\n",
    "init_theta = np.array([[1],[1]])  #init the theta\n",
    "J,grad = linearRegCostFunction(XX,y,init_theta,1.0)\n",
    "print 'Cost at theta = [1 ; 1]: (this value should be about 303.993192)'\n",
    "print J\n",
    "print 'Gradient at theta = [1 ; 1](this\\\n",
    " value should be about [-15.303016; 598.250744])'\n",
    "print grad\n",
    "\n",
    "\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n         Current function value: 22.373906\n         Iterations: 2\n         Function evaluations: 5\n         Gradient evaluations: 5\nresult = [ 13.08790351   0.36777923]\n"
     ]
    },
    {
     "data": {
      "image/png": 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//BUGIlJNlDGC9YA2BGMDGwD/I5h6or42Az6pdv9TYLcGvF6jsHKV0y1FAEw4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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9a9b358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import optimize\n",
    "\n",
    "def f(params,*args):\n",
    "    X,y,reg = args\n",
    "    m,n = X.shape\n",
    "    J = 0\n",
    "    theta = params.reshape((n,1))\n",
    "    theta1 = theta[1:,:]\n",
    "    J = 0.5 * np.sum((X.dot(theta)-y)**2) / m + reg * 0.5 * np.sum(theta1**2) / m\n",
    "\n",
    "    return J\n",
    "\n",
    "def gradf(params,*args):\n",
    "    X,y,reg = args\n",
    "    m,n = X.shape\n",
    "    theta = params.reshape((n,1))\n",
    "    grad = np.zeros_like(theta)\n",
    "    theta1 = theta[1:,:]\n",
    "    grad = X.T.dot(X.dot(theta) - y) / m\n",
    "    grad[1:,:] += reg * theta1 / m  #float / 1--->1.0\n",
    "    g = grad.ravel()\n",
    "    return g\n",
    "\n",
    "#Train linear regression with lambda = 0\n",
    "#用优化算法去训练\n",
    "def train(X,y,reg):\n",
    "    args = (X,y,reg)\n",
    "    inital_theta = np.zeros((X.shape[1],1))\n",
    "    params = inital_theta.ravel()\n",
    "    res = optimize.fmin_cg(f,x0=params,fprime=gradf,args=args,maxiter=500)\n",
    "    return res\n",
    "res = train(XX,y,0)\n",
    "print 'result =',res\n",
    "#可视化一下训练出来的参数res,也即theta权重参数\n",
    "#可以看出效果一般，因为是一个直线\n",
    "plt.plot(X,y,'rx',markersize= 10,linewidth= 1.5)\n",
    "plt.plot(X,XX.dot(res),'-')\n",
    "plt.xlabel('Change in water level (x)')\n",
    "plt.ylabel('Water flowing out of the dam (y)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n         Current function value: 0.000000\n         Iterations: 1\n         Function evaluations: 3\n         Gradient evaluations: 3\nOptimization terminated successfully.\n         Current function value: 0.000000\n         Iterations: 2\n         Function evaluations: 6\n         Gradient evaluations: 6\nOptimization terminated successfully.\n         Current function value: 3.286595\n         Iterations: 9\n         Function evaluations: 15\n         Gradient evaluations: 15\nOptimization terminated successfully.\n         Current function value: 2.842678\n         Iterations: 8\n         Function evaluations: 14\n         Gradient evaluations: 14\nOptimization terminated successfully.\n         Current function value: 13.154049\n         Iterations: 22\n         Function evaluations: 34\n         Gradient evaluations: 34\nOptimization terminated successfully.\n         Current function value: 19.443963\n         Iterations: 22\n         Function evaluations: 34\n         Gradient evaluations: 34\nOptimization terminated successfully.\n         Current function value: 20.098522\n         Iterations: 18\n         Function evaluations: 28\n         Gradient evaluations: 28\nOptimization terminated successfully.\n         Current function value: 18.172859\n         Iterations: 2\n         Function evaluations: 5\n         Gradient evaluations: 5\nOptimization terminated successfully.\n         Current function value: 22.609405\n         Iterations: 2\n         Function evaluations: 5\n         Gradient evaluations: 5\nOptimization terminated successfully.\n         Current function value: 23.261462\n         Iterations: 2\n         Function evaluations: 5\n         Gradient evaluations: 5\nOptimization terminated successfully.\n         Current function value: 24.317250\n         Iterations: 2\n         Function evaluations: 5\n         Gradient evaluations: 5\nOptimization terminated successfully.\n         Current function value: 22.373906\n         Iterations: 2\n         Function evaluations: 5\n         Gradient evaluations: 5\n[3.944304526105059e-31, 2.8596207814261678e-30, 3.2865950455018744, 2.8426776893998005, 13.154048809153679]\n[205.12109574547353, 110.30036610764685, 45.010231810301832, 48.368911369819756, 35.865141123151375]\n"
     ]
    },
    {
     "data": {
      "image/png": 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PjALWuvtNZnY10N3dr2poXUoQaUyaFO5quu22cHJOTQDV1SFJJOvWbfeTf+rQ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\nIEREJC0lCBERSUsJQkRE0lKCEBGRtP4/DUpZzibTq5YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9ba2dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#定义一下学习曲线，观察数据集大小m的变化对训练误差和验证误差的影响\n",
    "def learnCurve(X,y,Xval,yval,reg):\n",
    "    m = X.shape[0]\n",
    "    err_train = []\n",
    "    err_val = []\n",
    "    for i in xrange(m): #increase the data size :1--->m(m=12)\n",
    "        best_theta = train(X[:i+1,:],y[0:i+1],reg)\n",
    "        err_t,g1 = linearRegCostFunction(X[0:i+1,:],y[0:i+1],best_theta,reg)\n",
    "        err_v,g2= linearRegCostFunction(Xval,yval,best_theta,reg)\n",
    "        err_train.append(err_t)\n",
    "        err_val.append(err_v)\n",
    "    return err_train,err_val\n",
    "\n",
    "err_train,err_val = learnCurve(XX,y,XXval,yval,0)\n",
    "print err_train[:5]\n",
    "print err_val[:5]\n",
    "#可视化一下训练误差err_train和验证误差err_val的变化\n",
    "plt.plot(err_train,'b',linestyle = '-',label = 'err_train')\n",
    "plt.plot(err_val,'r',linestyle = '-',label = 'err_val')\n",
    "plt.xlabel('Number of training examples(m)')\n",
    "plt.ylabel('error')\n",
    "plt.title('Learning curve for linear regression')\n",
    "plt.legend(loc = 'upper left')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ -5.08542635e+00   8.48904834e+02  -1.28290173e+04   1.28967789e+06\n  -2.98314592e+07   2.29330301e+09  -6.84527284e+10   4.42233759e+12]\n[  2.86887308e+01   7.54346385e+02   4.61380464e+04   1.66104441e+06\n   8.99399404e+07   3.68940106e+09   1.89508052e+11   8.31905350e+12]\n[ 1.         -0.8389201   0.0013142  -0.25896174 -0.34156482  0.09754927\n -0.45519664  0.26677343 -0.46887381]\n"
     ]
    }
   ],
   "source": [
    "#从上面的图形看出，模型属于“高偏差”，那么增大数据集没有用，只能够增加模型复杂度，改进模型\n",
    "#所以增加多项式或者高次项特征\n",
    "def ployFeatures(X,p=8):\n",
    "    '''X is a vector'''\n",
    "    X_ploy = np.zeros((X.shape[0],p))\n",
    "    for i in xrange(p):\n",
    "        X_ploy[:,i] = X.T**(i+1)\n",
    "    return X_ploy\n",
    "\n",
    "#因为有高次项，所以进行特征均值归一化，进行特征缩放\n",
    "def featureNormalize(x):\n",
    "    mu = np.mean(x,axis=0)\n",
    "    xx = x - mu\n",
    "    sigma = np.std(x,axis=0)\n",
    "    x_norm = xx / sigma\n",
    "    return x_norm,mu,sigma\n",
    "X_ploy = ployFeatures(X,p=8)\n",
    "X_ploy,mu,sigma = featureNormalize(X_ploy)\n",
    "X_ploy = np.hstack((np.ones((X.shape[0],1)),X_ploy))\n",
    "print mu #correct\n",
    "print sigma\n",
    "print X_ploy[1,:]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12L, 9L) (21L, 9L) (21L, 9L)\n"
     ]
    }
   ],
   "source": [
    "X_ploy_test = ployFeatures(Xtest,p=8)\n",
    "X_ploy_test = (X_ploy_test - mu) / sigma #都是用训练集的mu,和sigma去缩放\n",
    "X_ploy_test = np.hstack((np.ones((Xtest.shape[0],1)),X_ploy_test))\n",
    "\n",
    "X_ploy_val = ployFeatures(Xval,p=8)\n",
    "X_ploy_val = (X_ploy_val - mu) / sigma\n",
    "X_ploy_val = np.hstack((np.ones((Xval.shape[0],1)),X_ploy_val))\n",
    "\n",
    "print X_ploy.shape,X_ploy_test.shape,X_ploy_val.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Maximum number of iterations has been exceeded.\n         Current function value: 0.036248\n         Iterations: 500\n         Function evaluations: 934\n         Gradient evaluations: 934\n[ 11.21756451   9.90756794  19.77561411  21.01763445 -36.70150507\n -52.39888966  28.56695973  42.27227577   3.23441143]\n"
     ]
    },
    {
     "data": {
      "image/png": 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L0BhTpGbMmMGll15K2bJlSUpKsiRgPFUW9xSRDcAm4CtgM86dgjEmykyaNInr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\nLBEYY0yMs0RgjDExzhKBMcbEuP8H0Z6Svd6pP24AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98d4080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#正则化强度=0,等于没有用正则化，容易过拟合\n",
    "res1 = train(X_ploy,y,0)\n",
    "print res1\n",
    "#我们可视化一下拟合的曲线,会发现过拟合了，所以需要选择合适的reg,正则化强度这个超参数\n",
    "def plotFit(mu,sigma,theta,p):\n",
    "    x = np.linspace(-50,45).reshape(-1,1)\n",
    "    x_ploy = ployFeatures(x,p)\n",
    "    x_ploy = x_ploy - mu\n",
    "    x_ploy = x_ploy / sigma\n",
    "    x_ploy = np.hstack((np.ones((x.shape[0],1)),x_ploy))\n",
    "    plt.plot(x,x_ploy.dot(theta),'--',color='black')\n",
    "\n",
    "    pass\n",
    "\n",
    "plt.plot(X,y,'rx',markersize= 10,linewidth= 1.5)\n",
    "plotFit(mu,sigma,res1,p=8)\n",
    "\n",
    "plt.xlabel('Change in water level (x)')\n",
    "plt.ylabel('Water flowing out of the dam (y)')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n         Current function value: 0.000000\n         Iterations: 2\n         Function evaluations: 4\n         Gradient evaluations: 4\nOptimization terminated successfully.\n         Current function value: 0.000000\n         Iterations: 6\n         Function evaluations: 9\n         Gradient evaluations: 9\nOptimization terminated successfully.\n         Current function value: 0.000000\n         Iterations: 15\n         Function evaluations: 27\n         Gradient evaluations: 27\nOptimization terminated successfully.\n         Current function value: 0.000000\n         Iterations: 4\n         Function evaluations: 13\n         Gradient evaluations: 13\nOptimization terminated successfully.\n         Current function value: 0.000000\n         Iterations: 17\n         Function evaluations: 35\n         Gradient evaluations: 35\nOptimization terminated successfully.\n         Current function value: 0.000000\n         Iterations: 138\n         Function evaluations: 268\n         Gradient evaluations: 268\nOptimization terminated successfully.\n         Current function value: 0.000000\n         Iterations: 32\n         Function evaluations: 68\n         Gradient evaluations: 68\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Maximum number of iterations has been exceeded.\n         Current function value: 0.013916\n         Iterations: 500\n         Function evaluations: 919\n         Gradient evaluations: 919\nWarning: Maximum number of iterations has been exceeded."
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n         Current function value: 0.000240\n         Iterations: 500\n         Function evaluations: 939\n         Gradient evaluations: 939\nWarning: Maximum number of iterations has been exceeded.\n         Current function value: 0.033273\n         Iterations: 500\n         Function evaluations: 921\n         Gradient evaluations: 921\nWarning: Desired error not necessarily achieved due to precision loss.\n         Current function value: 0.033852\n         Iterations: 393\n         Function evaluations: 761\n         Gradient evaluations: 749\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Maximum number of iterations has been exceeded.\n         Current function value: 0.036248\n         Iterations: 500\n         Function evaluations: 934\n         Gradient evaluations: 934\n[0.0, 9.8607613152626476e-32, 4.6174429281007728e-11, 2.8102318141054581e-20, 1.2849842344335099e-16]\n[161.442168317425, 160.79229150111109, 67.08492232193683, 67.726849416925191, 6.6169871317870843]\n"
     ]
    },
    {
     "data": {
      "image/png": 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Fr7jPIGIaECLleBB77hnGgzj77DBTixZQWcmgc8/d7rLOPfdcxo4dy9VXX83YsWMZO3Ys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\nlDxBOOecS6m+J4hRcQeQRb5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      "text/plain": [
       "<matplotlib.figure.Figure at 0x9830710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#在这之前还是绘制一下这个模型的学习曲线，看看模型方差和偏差怎么样\n",
    "err_train,err_val = learnCurve(X_ploy,y,X_ploy_val,yval,0)\n",
    "print err_train[:5]\n",
    "print err_val[:5]\n",
    "\n",
    "plt.plot(err_train,'b',linestyle = '-',label = 'err_train')\n",
    "plt.plot(err_val,'r',linestyle = '-',label = 'err_val')\n",
    "plt.xlabel('Number of training examples(m)')\n",
    "plt.ylabel('error')\n",
    "plt.title('Learning curve for linear regression')\n",
    "plt.legend(loc = 'upper left')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Maximum number of iterations has been exceeded.\n         Current function value: 0.036248\n         Iterations: 500\n         Function evaluations: 934\n         Gradient evaluations: 934\nWarning: Desired error not necessarily achieved due to precision loss.\n         Current function value: 0.178862\n         Iterations: 93\n         Function evaluations: 185\n         Gradient evaluations: 173\nWarning: Desired error not necessarily achieved due to precision loss.\n         Current function value: 0.243176\n         Iterations: 299\n         Function evaluations: 584\n         Gradient evaluations: 572\nOptimization terminated successfully.\n         Current function value: 0.371282\n         Iterations: 209\n         Function evaluations: 398\n         Gradient evaluations: 398\nOptimization terminated successfully.\n         Current function value: 0.636703\n         Iterations: 130\n         Function evaluations: 234\n         Gradient evaluations: 234\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n         Current function value: 1.360572\n         Iterations: 63\n         Function evaluations: 122\n         Gradient evaluations: 122\nOptimization terminated successfully.\n         Current function value: 2.917649\n         Iterations: 48\n         Function evaluations: 83\n         Gradient evaluations: 83\nOptimization terminated successfully.\n         Current function value: 6.830463\n         Iterations: 34\n         Function evaluations: 62\n         Gradient evaluations: 62\nOptimization terminated successfully.\n         Current function value: 14.937646\n         Iterations: 13\n         Function evaluations: 24\n         Gradient evaluations: 24\nOptimization terminated successfully.\n         Current function value: 31.878154\n         Iterations: 15\n         Function evaluations: 25\n         Gradient evaluations: 25\n"
     ]
    },
    {
     "data": {
      "image/png": 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SzEgCkC4lJiKakCAR8xHMnTuXCy+8kK+++gqAhQsXcuqpp/Ldd9/Rr18/3nnnHTZs2MBR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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xadfa3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#从上图可以看出，模型属于高方差，过拟合了，所以需要加入正则化,reg就不能等于0了\n",
    "#选择多少合适，就需要交叉验证来决定了\n",
    "def validationCurve(X,y,Xval,yval):\n",
    "    lambda_vec = [0,0.001,0.003,0.01,0.03,0.1,0.3,1.0,3.0,10.0] #1,3,10-->1.0,3.0,10.0\n",
    "    err_train = []\n",
    "    err_val = []\n",
    "    for reg in lambda_vec: #choice the reg\n",
    "        best_theta = train(X,y,reg)\n",
    "        err_t,g1 = linearRegCostFunction(X,y,best_theta,reg)\n",
    "        err_v,g2= linearRegCostFunction(Xval,yval,best_theta,reg)\n",
    "        err_train.append(err_t)\n",
    "        err_val.append(err_v)\n",
    "    return lambda_vec,err_train,err_val\n",
    "\n",
    "lambda_vec,err_train,err_val = validationCurve(X_ploy,y,X_ploy_val,yval) \n",
    "plt.plot(lambda_vec,err_train,'b',linestyle = '-',label = 'err_train')\n",
    "plt.plot(lambda_vec,err_val,'r',linestyle = '-',label = 'err_val')\n",
    "plt.xlabel('the lamda(reg)')\n",
    "plt.ylabel('error')\n",
    "plt.title('Learning curve for linear regression')\n",
    "plt.legend(loc = 'upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "reg\terr_train\terr_val\n0.000000\t0.036248\t26.937810\n0.001000\t0.178862\t16.253146\n0.003000\t0.243176\t16.075527\n0.010000\t0.371282\t17.235271\n0.030000\t0.636703\t13.421113\n0.100000\t1.360572\t8.453900\n0.300000\t2.917649\t5.932013\n1.000000\t6.830463\t7.047226\n3.000000\t14.937646\t9.782200\n10.000000\t31.878154\t18.633922\n"
     ]
    }
   ],
   "source": [
    "#打印对比一下err_train和err_val\n",
    "print 'reg\\terr_train\\terr_val'\n",
    "for i in xrange(len(lambda_vec)):\n",
    "    print '%f\\t%f\\t%f' %(lambda_vec[i],err_train[i],err_val[i])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n         Current function value: 2.917649\n         Iterations: 48\n         Function evaluations: 83\n         Gradient evaluations: 83\n[ 11.21759788  10.36108651   6.90555014   2.55156851   1.33110548\n   0.41366221  -0.06161811   0.28647949  -0.61899355]\n"
     ]
    },
    {
     "data": {
      "image/png": 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V/XMxm2woozGllZYGSUmQnMz+/fupUqUKFStW5Pbbb6dp06Z07drVmW84MxOG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\nt8TK+cfovBsdgH7AtyLyX3f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      "text/plain": [
       "<matplotlib.figure.Figure at 0xafd7d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#so good reg is 0.3,结果会平滑一点，不会太过拟合\n",
    "res1 = train(X_ploy,y,reg=0.3)\n",
    "print res1\n",
    "#可视化一下拟合的曲面,发现更加平滑了，不会过拟合\n",
    "def plotFit(mu,sigma,theta,p):\n",
    "    x = np.linspace(-50,45).reshape(-1,1)\n",
    "    x_ploy = ployFeatures(x,p)\n",
    "    x_ploy = x_ploy - mu\n",
    "    x_ploy = x_ploy / sigma\n",
    "    x_ploy = np.hstack((np.ones((x.shape[0],1)),x_ploy))\n",
    "    plt.plot(x,x_ploy.dot(theta),'--',color='black')\n",
    "\n",
    "    pass\n",
    "\n",
    "plt.plot(X,y,'rx',markersize= 10,linewidth= 1.5)\n",
    "plotFit(mu,sigma,res1,p=8)\n",
    "\n",
    "plt.xlabel('Change in water level (x)')\n",
    "plt.ylabel('Water flowing out of the dam (y)')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}