coursera-machine-learning-python/ex2/ex2_reg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2-2: Logistic Regression with Regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this part of the exercise, we will implement regularized logistic regression to predict whether microchips from a fabrication plant passes quality assurance (QA)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In `ex2data2.txt`, the first two columns contains the X values and the third column contains the label y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "\n",
    "data = np.loadtxt(open(\"ex2data2.txt\", \"r\"), delimiter=\",\")\n",
    "X = data[:, 0:2]\n",
    "y = data[:, 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `plot_data()` is the same as in the last exercise (Exercise 2-1: Logistic Regression)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def plot_data(X, y):\n",
    "    \"\"\"\n",
    "    Plots the data points X and y.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    X : array-like, shape (n_samples, 2)\n",
    "        Data on x axis.\n",
    "    y : array-like, shape (n_samples,)\n",
    "        Data on y axis.\n",
    "    \"\"\"\n",
    "    pos = np.argwhere(y == 1)\n",
    "    neg = np.argwhere(y == 0)\n",
    "\n",
    "    plt.plot(X[pos, 0], X[pos, 1], linestyle='', marker='+', color='k')\n",
    "    plt.plot(X[neg, 0], X[neg, 1], linestyle='', marker='o', color='y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SYWjiXO+FsVAo0NGxmJaWqcydO4WWlql0dCymUCjU9b5pEFbSUMn7RHUcNSeMiFQrizUs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\n6v1/0KdRPg5oV2EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10982bb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plot_data(X, y)\n",
    "plt.xlabel('Microchip Test 1')\n",
    "plt.ylabel('Microchip Test 2')\n",
    "plt.legend(['y = 1', 'y = 0'], loc='upper right', numpoints=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Regularized Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `map_feature()` maps input features to polynomial ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def map_feature(X1, X2):\n",
    "    \"\"\"\n",
    "    Feature mapping function to polynomial features. Inputs X1, X2 must be the same size.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    X1 : ndarray, shape (n_samples,)\n",
    "        Input feature.\n",
    "    X2 : ndarray, shape (n_samples,)\n",
    "        Input feature.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    Out : ndarray, shape (n_samples, 28)\n",
    "        A new feature array with more features, comprising of X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..\n",
    "    \"\"\"\n",
    "    degree = 6\n",
    "    Out = np.ones(len(X1))\n",
    "\n",
    "    for i in range(1, degree + 1):\n",
    "        for j in range(0, i + 1):\n",
    "            tmp = np.power(X1, i - j) * np.power(X2, j)\n",
    "            Out = np.vstack((Out, tmp))\n",
    "    return Out.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add polynomial features: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Note that map_feature also adds a column of ones for us, so the intercept term is handled\n",
    "X = map_feature(X[:, 0], X[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize parameters as follows: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m, n = X.shape\n",
    "# Initialize fitting parameters\n",
    "initial_theta = np.zeros(n)\n",
    "# Set regularization parameter lambda to 1\n",
    "l = 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `cost_function_reg()` computes the cost and gradient for logistic regression with regularization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cost_function_reg(theta, X, y, l):\n",
    "    \"\"\"\n",
    "    Compute cost and gradient for logistic regression with regularization.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    theta : ndarray, shape (n_features,)\n",
    "        Linear regression parameter.\n",
    "    X : ndarray, shape (n_samples, n_features)\n",
    "        Training data, where n_samples is the number of samples and n_features is the number of features.\n",
    "    y : ndarray, shape (n_samples,)\n",
    "        Labels.\n",
    "    l : float\n",
    "        Regularization parameter.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    J : numpy.float64\n",
    "        The cost of using theta as the parameter for regularized logistic regression w.r.t. the parameters.\n",
    "    grad: ndarray, shape (n_features,)\n",
    "        Partial derivatives of the cost w.r.t. each parameter in theta.\n",
    "    \"\"\"\n",
    "    m, n = X.shape\n",
    "\n",
    "    x_dot_theta = X.dot(theta)\n",
    "    mask = np.eye(len(theta))\n",
    "    # Skip the theta[0, 0] parameter when performing regularization\n",
    "    mask[0, 0] = 0\n",
    "\n",
    "    J = 1.0 / m * (np.dot(-y.T, np.log(sigmoid(x_dot_theta))) - np.dot((1 - y).T, np.log(1 - sigmoid(x_dot_theta)))) \\\n",
    "        + 1.0 * l / (2 * m) * np.sum(np.power((mask.dot(theta)), 2))\n",
    "\n",
    "    grad = 1.0 / m * np.dot((sigmoid(x_dot_theta) - y).T, X).T + 1.0 * l / m * (mask.dot(theta))\n",
    "\n",
    "    return J, grad\n",
    "\n",
    "\n",
    "def sigmoid(z):\n",
    "    \"\"\"\n",
    "    Compute sigmoid function.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    z : array-like\n",
    "        Variable for sigmoid function.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    ndarray\n",
    "        The sigmoid of each value of z.\n",
    "    \"\"\"\n",
    "    g = 1 / (1 + np.exp(-z))\n",
    "    return g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test `cost_function_reg()` on inital parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at initial theta (zeros): 0.69314718056\n"
     ]
    }
   ],
   "source": [
    "cost, _ = cost_function_reg(initial_theta, X, y, l)\n",
    "print 'Cost at initial theta (zeros):', cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Regularization and Accuracies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train the model with `fin_tnc()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.optimize as opt\n",
    "\n",
    "\n",
    "theta, nfeval, rc = opt.fmin_tnc(func=cost_function_reg, x0=initial_theta, args=(X, y, l))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the decision boundary: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WP0oGR0YeZMaMz+jcOQWt4cqVkvtOTj5Hamomffo0Af6YefTpp7/Qtm09mjcP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\ne+wKcFhrvdG40ER1GFnxMz7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jxy+4OBIhqt7C8qRDoxCm1717ONdcU4ePPvpZEhYhTMSR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\nnhIWERER8T0lLCIiIuJ7/wfpEVdUDqsP7AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e4bca50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from plot_decision_boundary import plot_decision_boundary\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plot_data(X[:, 1:], y)\n",
    "plt.xlabel('Microchip Test 1')\n",
    "plt.ylabel('Microchip Test 2')\n",
    "plt.legend(['y = 1', 'y = 0'], loc='upper right', numpoints=1)\n",
    "plot_decision_boundary(theta, X, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `predict()` predicts the input data with learned logistic regression parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def predict(theta, X):\n",
    "    \"\"\"\n",
    "    Predict whether the label is 0 or 1 using learned logistic regression parameters theta.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    theta : ndarray, shape (n_features,)\n",
    "        Linear regression parameter.\n",
    "    X : ndarray, shape (n_samples, n_features)\n",
    "        Training data, where n_samples is the number of samples and n_features is the number of features.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    ndarray, shape (n_samples,)\n",
    "        The predictions for X using a threshold at 0.5.\n",
    "    \"\"\"\n",
    "    p = sigmoid(X.dot(theta)) >= 0.5\n",
    "    return p.astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute accuracy on the training set: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Accuracy: 83.0508474576\n"
     ]
    }
   ],
   "source": [
    "p = predict(theta, X)\n",
    "print 'Train Accuracy:', np.mean(p == y) * 100"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}