Linear regression and polynomial regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 22.373906\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io #Used to load the OCTAVE *.mat files\n",
    "from scipy.optimize import *\n",
    "\n",
    "def plotData():\n",
    "    plt.figure(figsize=(8,5))\n",
    "    plt.ylabel('Water flowing out of the dam (y)')\n",
    "    plt.xlabel('Change in water level (x)')\n",
    "    plt.plot(X[:,1],y,'rx')\n",
    "    plt.grid(True)\n",
    "    \n",
    "datafile = 'E:\\Mat_Work\\machine-learning-ex5\\ex5\\ex5data1.mat'\n",
    "mat = scipy.io.loadmat( datafile )\n",
    "X = mat.get(\"X\")\n",
    "y = mat.get(\"y\")\n",
    "ytest = mat.get(\"ytest\")\n",
    "yval = mat.get(\"yval\")\n",
    "Xtest = mat.get(\"Xtest\")\n",
    "Xval = mat.get(\"Xval\")\n",
    "\n",
    "def linearRegCostFunction(init_theta,X,y,reg):\n",
    "    m = len(y)\n",
    "    # Make theta 2-d to get cost and gradient\n",
    "    theta = init_theta[:,None]\n",
    "    cost = ((np.sum((np.dot(X,theta) - y)**2))/(2*m) + (reg/(2*m))*np.sum(theta**2))\n",
    "\n",
    "    # Regularized \n",
    "    gradients = ((np.sum((np.dot(X,theta)-y)*X,axis=0)/m)+(reg/m)*theta.T)\n",
    "\n",
    "    # Replace gradient for theta_0 with non-regularized\n",
    "    gradients[0] = gradients[0] - (reg/m)*theta.T\n",
    "    gradients = gradients.flatten()\n",
    "\n",
    "    return (cost, gradients)\n",
    "\n",
    "def trainLinearReg(X,y,reg):\n",
    "    initial_theta = np.zeros(np.size(X,1))\n",
    "    res = minimize(linearRegCostFunction,initial_theta,args=(X,y,reg),jac=True,options={'maxiter':400,'disp':True})\n",
    "    return res.x\n",
    "\n",
    "def learningCurve(X,y,Xval,yval,reg):\n",
    "    m_train = len(X)\n",
    "    m_val = len(Xval)\n",
    "    error_train = np.zeros(m_train)\n",
    "    error_val = np.zeros(m_train)\n",
    "    for i in range(1,m_train+1):\n",
    "        est_theta = trainLinearReg(X[0:i],y[0:i],reg)\n",
    "        error_train[i-1] = (np.sum((np.dot(X[0:i],est_theta)-y[0:i])**2))/(2.0*i)\n",
    "        error_val[i-1] = (np.sum((np.dot(Xval,est_theta)-yval)**2))/(2.0*m_val)\n",
    "\n",
    "    return (error_train, error_val)\n",
    "\n",
    "def polyFeatures(X,p):\n",
    "    X_poly = np.zeros((len(X),p))\n",
    "    X = X.flatten()\n",
    "    for i in range(1,p+1):\n",
    "        X_poly[:,i-1] = X**i\n",
    "    return X_poly\n",
    "\n",
    "def featureNormalize(X):\n",
    "    mu = np.mean(X,axis=0)\n",
    "    sigma = np.std(X,axis=0)\n",
    "    normalized_X = np.divide(X - mu,sigma)\n",
    "\n",
    "    return (normalized_X, mu, sigma)\n",
    "\n",
    "def plotFit(min_x, max_x, mu, sigma, theta, p):\n",
    "    x = np.arange(min_x - 15, max_x + 25, 0.05).reshape((-1,1))\n",
    "    X_poly = polyFeatures(x,p)\n",
    "    X_poly = np.divide(X_poly - mu, sigma)\n",
    "    X_poly = np.hstack((np.ones(len(X_poly)).reshape((-1,1)),X_poly))\n",
    "    plt.plot(x,np.dot(X_poly,theta),'b--',linewidth=2)\n",
    "    return\n",
    "\n",
    "def validationCurve(X, y, Xval, yval):\n",
    "    lambda_vec = np.array([0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10]).reshape((-1,1))\n",
    "    error_train = np.zeros(len(lambda_vec))\n",
    "    error_val = np.zeros(len(lambda_vec))\n",
    "\n",
    "    for i in range(len(lambda_vec)):\n",
    "        m_train = len(X)\n",
    "        m_val = len(Xval)\n",
    "        reg_param = lambda_vec[i]\n",
    "        est_theta = trainLinearReg(X,y,reg_param)\n",
    "        error_train[i] = (np.sum((np.dot(X,est_theta)-y)**2))/(2.0*m_train)\n",
    "        error_val[i] = (np.sum((np.dot(Xval,est_theta)-yval)**2))/(2.0*m_val)\n",
    "\n",
    "    return (lambda_vec, error_train, error_val)\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",
    "# Regularized Cost\n",
    "full_X = np.hstack((np.ones_like(y), X))\n",
    "theta = np.array([1,1])\n",
    "J, g = linearRegCostFunction(theta,full_X,y,0.0)\n",
    "\n",
    "# Reguliarized Gradient\n",
    "J, g = linearRegCostFunction(theta,full_X,y,1.0)\n",
    "\n",
    "# Train Linear Regression\n",
    "reg_param = 0\n",
    "est_theta = trainLinearReg(full_X,y,reg_param)\n",
    "\n",
    "# Plot linear fit \n",
    "plt.plot(X, y, 'rx', markersize=10, linewidth=1.5)\n",
    "plt.plot(X,np.dot(full_X,est_theta),'b-',linewidth=2)\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": 23,
   "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\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 3\n",
      "         Function evaluations: 6\n",
      "         Gradient evaluations: 6\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 3.286595\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 2.842678\n",
      "         Iterations: 5\n",
      "         Function evaluations: 6\n",
      "         Gradient evaluations: 6\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 13.154049\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 19.443963\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 20.098522\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 18.172859\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 22.609405\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 23.261462\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 24.317250\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 22.373906\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Learning Curve\n",
    "reg_param = 0.0\n",
    "full_Xval = np.hstack((np.ones_like(yval),Xval))\n",
    "error_train, error_val = learningCurve(full_X,y,full_Xval,yval,reg_param)\n",
    "\n",
    "plt.plot(range(len(X)), error_train, range(len(X)), error_val)\n",
    "plt.title('Learning curve for linear regression')\n",
    "plt.legend(['Train', 'Cross Validation'])\n",
    "plt.xlabel('Number of training examples')\n",
    "plt.ylabel('Error')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Feature Mapping For Polynomial Regression\n",
    "p = 8\n",
    "X_poly = polyFeature(X,p)\n",
    "X_poly, mu, sigma = featureNormalize(X_poly)\n",
    "X_poly = np.hstack((np.ones_like(y),X_poly))\n",
    "\n",
    "X_poly_test = polyFeatures(Xtest,p)\n",
    "X_poly_test = np.divide(X_poly_test - mu, sigma)\n",
    "X_poly_test = np.hstack((np.ones_like(ytest),X_poly_test))\n",
    "\n",
    "X_poly_val = polyFeatures(Xval,p)\n",
    "X_poly_val = np.divide(X_poly_val - mu, sigma)\n",
    "X_poly_val = np.hstack((np.ones_like(yval),X_poly_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 12.629773\n",
      "         Iterations: 6\n",
      "         Function evaluations: 105\n",
      "         Gradient evaluations: 93\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 0.560050\n",
      "         Iterations: 1\n",
      "         Function evaluations: 107\n",
      "         Gradient evaluations: 95\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 0.299658\n",
      "         Iterations: 1\n",
      "         Function evaluations: 112\n",
      "         Gradient evaluations: 100\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 29.160792\n",
      "         Iterations: 4\n",
      "         Function evaluations: 136\n",
      "         Gradient evaluations: 123\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 21.671558\n",
      "         Iterations: 4\n",
      "         Function evaluations: 104\n",
      "         Gradient evaluations: 92\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 21.611369\n",
      "         Iterations: 5\n",
      "         Function evaluations: 109\n",
      "         Gradient evaluations: 97\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 18.000995\n",
      "         Iterations: 5\n",
      "         Function evaluations: 96\n",
      "         Gradient evaluations: 84\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 17.513278\n",
      "         Iterations: 6\n",
      "         Function evaluations: 107\n",
      "         Gradient evaluations: 95\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 15.510485\n",
      "         Iterations: 6\n",
      "         Function evaluations: 110\n",
      "         Gradient evaluations: 98\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 13.863191\n",
      "         Iterations: 7\n",
      "         Function evaluations: 106\n",
      "         Gradient evaluations: 94\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 12.646442\n",
      "         Iterations: 6\n",
      "         Function evaluations: 61\n",
      "         Gradient evaluations: 50\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 11.528491\n",
      "         Iterations: 6\n",
      "         Function evaluations: 50\n",
      "         Gradient evaluations: 40\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 12.629773\n",
      "         Iterations: 6\n",
      "         Function evaluations: 105\n",
      "         Gradient evaluations: 93\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Learning Curve for polynomial regression\n",
    "reg_param = 1.0\n",
    "est_theta = trainLinearReg(X_poly,y,reg_param)\n",
    "plt.plot(X, y, 'rx', markersize=10, linewidth=1.5)\n",
    "plotFit(np.min(X), np.max(X), mu, sigma, est_theta, p)\n",
    "plt.xlabel('Change in water level (x)')\n",
    "plt.ylabel('Water flowing out of the dam (y)')\n",
    "plt.show()\n",
    "\n",
    "error_train, error_val = learningCurve(X_poly,y,X_poly_val,yval,reg_param)\n",
    "plt.plot(range(len(X)), error_train, range(len(X)), error_val);\n",
    "plt.title('Learning curve for polinomial regression')\n",
    "plt.legend(['Train', 'Cross Validation'])\n",
    "plt.xlabel('Number of training examples')\n",
    "plt.ylabel('Error')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 22.373906\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 22.381049\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 22.395335\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 22.445335\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 22.588192\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 23.088192\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 24.516762\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 29.516760\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 43.802466\n",
      "         Iterations: 3\n",
      "         Function evaluations: 5\n",
      "         Gradient evaluations: 5\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 60.842378\n",
      "         Iterations: 3\n",
      "         Function evaluations: 50\n",
      "         Gradient evaluations: 39\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Validation for selecting lambda\n",
    "lambda_vec, error_train, error_val = validationCurve(full_X,y,full_Xval,yval)\n",
    "\n",
    "plt.plot(lambda_vec, error_train, lambda_vec, error_val);\n",
    "plt.title('Selecting \\lambda using a cross validation set')\n",
    "plt.legend(['Train', 'Cross Validation'])\n",
    "plt.xlabel('lambda')\n",
    "plt.ylabel('Error')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}