Linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "22OuOZtax7MB"
   },
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
    "matplotlib.rcParams['xtick.direction'] = 'out'\n",
    "matplotlib.rcParams['ytick.direction'] = 'out'\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bGLfhS4Jx7MF"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.5 2. ]\n",
      "Eigen values of Hessian matrix:  [2.05189714 0.06870891]\n",
      "First eigen vector of Hessian matrix:  [0.99998927 0.00463202]\n",
      "Second eigen vector of Hessian matrix:  [-0.00463202  0.99998927]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert least squares problem to quadratic. \n",
    "# Give a plot illustrating the least squares problem.\n",
    "\n",
    "delta=0.025\n",
    "x = np.arange(-4.0, 4.0, delta)\n",
    "y = np.arange(-4.0, 4.0, delta)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = 0.5*X+2*Y   # Income is truly 0.5* height + 2*weight (but we don't know yet)\n",
    "true_w = np.array([0.5,2])\n",
    "levels = np.linspace(Z.min(), Z.max(), 50)\n",
    "plt.figure(figsize=(18,10))\n",
    "plt.axis('equal')\n",
    "CS = plt.contourf(X, Y, Z, levels=levels, cmap=\"viridis\")\n",
    "plt.colorbar()\n",
    "plt.xlabel('Height')\n",
    "plt.ylabel('Weight')\n",
    "plt.title('Estimating average income as a function of height and weight')\n",
    "\n",
    "num_samples=100\n",
    "x=np.random.rand(num_samples,2)-0.5   \n",
    "data_transform=np.array([[5,0],[0,1]])  \n",
    "\n",
    "x=np.dot(data_transform, x.T).T # The heights and weights of num_samples people\n",
    "y = np.dot(x,true_w) + 0.0*np.random.randn(num_samples) # The incomes of num_samples people \n",
    "\n",
    "plt.scatter(x[:,0],x[:,1],color='r', marker='x')\n",
    "\n",
    "A = np.dot(x.T,x)/num_samples\n",
    "b = np.dot(y,x)/num_samples\n",
    "c = np.dot(y,y)/(2*num_samples)\n",
    "\n",
    "# print(A)\n",
    "# print(b)\n",
    "# print(c)\n",
    "\n",
    "# objective is 0.5* \\frac{1}{n} \\sum_{i=1}^n (w^\\top x_i - y_i)^2\n",
    "# which is equal to 0.5 * w^\\top A w - b^\\top w + c\n",
    "# Minimiser of above is given by solving Aw=b\n",
    "\n",
    "\n",
    "A_inv = np.linalg.inv(A)\n",
    "w_soln = np.dot(A_inv, b)\n",
    "print(w_soln)\n",
    "\n",
    "d,v = np.linalg.eig(A)\n",
    "# print(v)\n",
    "print(\"Eigen values of Hessian matrix: \", d)\n",
    "print(\"First eigen vector of Hessian matrix: \", v[:,0])\n",
    "print(\"Second eigen vector of Hessian matrix: \", v[:,1])\n",
    "\n",
    "smooth_coeff=d.max()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "HisQRcKLx7ML"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.05940972 3.8762762 ]\n",
      "[0.4943606  3.80605583]\n",
      "[0.48994848 3.68109476]\n",
      "[0.49698536 2.00356267]\n",
      "[0.49987031 2.00000109]\n",
      "[0.49999999 1.99999968]\n",
      "Quasi newton done\n",
      "[0.52970486 3.9381381 ]\n",
      "[0.37219697 3.67109271]\n",
      "[0.5573588  3.58580567]\n",
      "[0.42509954 3.47625232]\n",
      "[0.56522342 3.37544586]\n",
      "[0.4187595 3.2802828]\n",
      "[0.53495919 3.21482653]\n",
      "[0.45206853 3.13098429]\n",
      "[0.54002763 3.05366778]\n",
      "[0.44821768 2.98085888]\n",
      "[0.54545723 2.91389908]\n",
      "[0.46920715 2.86646198]\n",
      "[0.55204174 2.77753049]\n",
      "[0.46659833 2.73707968]\n",
      "[0.52836282 2.6867112 ]\n",
      "[0.46385825 2.63923826]\n",
      "[0.53214377 2.5956217 ]\n",
      "[0.47857444 2.56468785]\n",
      "[0.5173493  2.52606155]\n",
      "[0.47691861 2.48973468]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1296x1008 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Contour plots and gradient descent for minimising a quadratic:\n",
    "# f(w) = 0.5*w^\\top A w + b^\\top w + c\n",
    "\n",
    "delta=0.025\n",
    "\n",
    "x = np.arange(true_w[0]-4., true_w[0]+4.0, delta)\n",
    "y = np.arange(true_w[1]-4., true_w[1]+4.0, delta)\n",
    "\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "Z = np.zeros(X.shape)\n",
    "\n",
    "for i in range(Z.shape[0]):\n",
    "    for j in range(Z.shape[0]):\n",
    "        input_vec = np.array([X[i,j],Y[i,j]])\n",
    "#         input_vec = input_vec[:,None]\n",
    "        temp = np.dot(A, input_vec)\n",
    "        Z[i,j] = 0.5*np.dot(input_vec, np.dot(A, input_vec)) \n",
    "        Z[i,j] -= np.dot(b, input_vec) \n",
    "        Z[i,j] += c\n",
    "        \n",
    "\n",
    "levels = np.linspace(Z.min(), Z.max(), 50)\n",
    "\n",
    "plt.figure(figsize=(18,14))\n",
    "plt.axis('equal')\n",
    "CS = plt.contourf(X, Y, Z, levels=levels, cmap=\"hot\")\n",
    "plt.xlabel(\"Weight vector dimension 1 (Coefficient of height)\")\n",
    "plt.ylabel(\"Weight vector dimension 2 (Coefficient of weight)\")\n",
    "plt.title(\"Contour plot of least squares error for given data set\")\n",
    "plt.colorbar()\n",
    "plt.plot(true_w[0], true_w[1],'bo')\n",
    "\n",
    "num_iter=20\n",
    "\n",
    "w=np.array([-1., 4.])\n",
    "\n",
    "trajectory=np.zeros((2,num_iter))\n",
    "\n",
    "# Quasi Newton (BFGS)\n",
    "H =  np.eye(2)\n",
    "for i in range(num_iter):\n",
    "    trajectory[:,i]=w\n",
    "    grad = np.dot(A,w)-b\n",
    "    if np.linalg.norm(grad)< 1e-5:\n",
    "        break\n",
    "    direction = np.dot(H, grad)\n",
    "    value = 0.5*np.dot(w, np.dot(A, w)) - np.dot(b, w) + c\n",
    "#     eta=1.\n",
    "#     max_eta=np.inf\n",
    "#     min_eta=0.\n",
    "#     while True:\n",
    "#         w_cand = w - (eta)*direction\n",
    "#         f = 0.5*np.dot(w_cand, np.dot(A, w_cand)) - np.dot(b, w_cand) + c\n",
    "#         f1 = value - eta*0.5*np.sum(grad*grad)\n",
    "#         f2 = value - eta*0.25*np.sum(grad*grad)\n",
    "# #         print(eta,f,f1,f2)\n",
    "#         if f<f2 and f>f1:\n",
    "#             break\n",
    "#         if f>f2:\n",
    "#             max_eta = eta\n",
    "#             eta = (eta+min_eta)/2\n",
    "#         if f<f1:\n",
    "#             min_eta = eta\n",
    "#             eta = min(2.*eta, (eta+max_eta)/2.)\n",
    "    w_cand = w - direction\n",
    "    s = w_cand - w\n",
    "    y = np.dot(A,w_cand)-b - grad\n",
    "    \n",
    "    rho =  1/np.dot(s,y)\n",
    "    mat1 = np.eye(2) - rho*np.dot(s[:,None],y[None,:])\n",
    "    mat2 = rho*np.dot(s[:,None],s[None,:])\n",
    "    H = np.dot(mat1,np.dot(H,mat1.T)) + mat2\n",
    "    w = w_cand\n",
    "#     print(eta)\n",
    "    print(w)\n",
    "\n",
    "plt.plot(trajectory[0,:i],trajectory[1,:i],'go-', markersize=15, linewidth=5)\n",
    "\n",
    "\n",
    "print(\"Quasi newton done\")\n",
    "# # Gradient descent\n",
    "\n",
    "trajectory=np.zeros((2,num_iter))\n",
    "w=np.array([-1., 4.])\n",
    "for i in range(num_iter):\n",
    "    trajectory[:,i]=w\n",
    "    grad = np.dot(A,w)-b\n",
    "    value = 0.5*np.dot(w, np.dot(A, w)) - np.dot(b, w) + c\n",
    "    eta=1\n",
    "    max_eta=np.inf\n",
    "    min_eta=0.\n",
    "    while True:\n",
    "        w_cand = w - (eta)*grad\n",
    "        f = 0.5*np.dot(w_cand, np.dot(A, w_cand)) - np.dot(b, w_cand) + c\n",
    "        f1 = value - eta*0.5*np.sum(grad*grad)\n",
    "        f2 = value - eta*0.25*np.sum(grad*grad)\n",
    "#         print(eta,f,f1,f2)\n",
    "        if f<f2 and f>f1:\n",
    "            break\n",
    "        if f>f2:\n",
    "            max_eta = eta\n",
    "            eta = (eta+min_eta)/2\n",
    "        if f<f1:\n",
    "            min_eta = eta\n",
    "            eta = min(2.*eta, (eta+max_eta)/2.)\n",
    "            \n",
    "    w = w_cand\n",
    "#     print(eta)\n",
    "    print(w)\n",
    "    \n",
    "\n",
    "# plt.plot(trajectory[0,:],trajectory[1,:],'rx-', markersize=15, linewidth=5)"
   ]
  }
 ],
 "metadata": {
  "colab": {
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