homework 7.8-7.10.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from random import random\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_random_points(n):\n",
    "    return np.random.uniform(-1, 1, [n, 2])\n",
    "\n",
    "def get_random_line_vector():\n",
    "    rp = np.random.uniform(-1, 1, (2, 2)) \n",
    "    slope = (rp[0, 1] - rp[1, 1]) / (rp[0, 0] - rp[1, 0])\n",
    "    intercept = rp[0, 1] - rp[0, 0] * slope\n",
    "    return [intercept, slope, 1]    \n",
    "\n",
    "def get_labels(pi, vector):\n",
    "    labels = np.sign(np.dot(pi, vector))\n",
    "    return labels\n",
    "\n",
    "def add_intercept(points):\n",
    "    pi = np.array([[1, x1, x2] for (x1, x2) in points])\n",
    "    return pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_initial_w():\n",
    "    w = np.array([0, 0 , 0.001])\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_perceptron_predictions(pi, labels, w):\n",
    "    return np.sign(np.dot(pi, w)) == labels\n",
    "\n",
    "def update_w(w, mp, label):\n",
    "    return w + label*mp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from itertools import count\n",
    "\n",
    "def train_perceptron(pi, labels, w): \n",
    "    for num_iterations in count(start=0, step=1):    \n",
    "        predictions = get_perceptron_predictions(pi, labels, w)\n",
    "\n",
    "        if predictions.all():\n",
    "            break\n",
    "\n",
    "        missclassified_points_indexes = np.where(predictions==False)[0]\n",
    "        k = np.random.choice(missclassified_points_indexes, 1)[0]\n",
    "        w = update_w(w, pi[k], labels[k])\n",
    "#         print(w)\n",
    "    return w, num_iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N_TEST = 10000\n",
    "points_test = get_random_points(N_TEST) # hack for speed\n",
    "pi_test = add_intercept(points_test)\n",
    "\n",
    "def evaluate_solution(w, fx_vector):\n",
    "    labels_test = get_labels(pi_test, fx_vector)\n",
    "    return get_perceptron_predictions(pi_test, labels_test, w).sum() / N_TEST"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fit_svm(x, y):\n",
    "    NUM = x.shape[0]\n",
    "    DIM = x.shape[1]\n",
    "    # we'll solve the dual\n",
    "    # obtain the kernel\n",
    "    K = y[:, None] * x\n",
    "    K = np.dot(K, K.T)\n",
    "    P = matrix(K)\n",
    "    q = matrix(-np.ones((NUM, 1)))\n",
    "    G = matrix(-np.eye(NUM))\n",
    "    h = matrix(np.zeros(NUM))\n",
    "    A = matrix(y.reshape(1, -1))\n",
    "    b = matrix(np.zeros(1))\n",
    "    solvers.options['show_progress'] = False\n",
    "    sol = solvers.qp(P, q, G, h, A, b)\n",
    "    alphas = np.array(sol['x'])\n",
    "    return alphas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_w_svm(alphas, points, labels):\n",
    "    # get weights\n",
    "    w_svm = np.sum(alphas * labels[:, None] * points, axis = 0)\n",
    "    # get bias\n",
    "    cond = (alphas > 1e-4).reshape(-1)\n",
    "    b = labels[cond] - np.dot(points[cond], w_svm)\n",
    "    bias = b[0]\n",
    "\n",
    "    # normalize\n",
    "    norm = np.linalg.norm(w_svm)\n",
    "    w_svm_norm, bias_norm = w_svm / norm, bias / norm\n",
    "\n",
    "    w_svm_final = [bias_norm, w_svm_norm[0], w_svm_norm[1]]\n",
    "    return w_svm_final"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare Perceptron to SVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def run_experiment(n):\n",
    "    # create points\n",
    "    points = get_random_points(n)\n",
    "    pi = add_intercept(points)\n",
    "    while True:\n",
    "        fx_vector = get_random_line_vector()\n",
    "        labels = get_labels(pi, fx_vector)\n",
    "        if (labels < 0).any() and (labels > 0).any():\n",
    "            break\n",
    "    \n",
    "    # train & evaluate pereceptron\n",
    "    w_perceptron = get_initial_w()\n",
    "    w_perceptron, iterations = train_perceptron(pi, labels, w_perceptron)\n",
    "    acc_perceptron = evaluate_solution(w_perceptron, fx_vector)\n",
    "    \n",
    "    # train & evaluate svm\n",
    "    alphas = fit_svm(points, labels)\n",
    "    w_svm = get_w_svm(alphas, points, labels)\n",
    "    acc_svm = evaluate_solution(w_svm, fx_vector)\n",
    "    \n",
    "    return acc_svm > acc_perceptron, sum(alphas > 1e-4)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.632\n",
      "2.843\n"
     ]
    }
   ],
   "source": [
    "RUNS = 1000\n",
    "N  = 10\n",
    "c = 0\n",
    "a = 0\n",
    "\n",
    "for i in range(RUNS):\n",
    "    ci, ai = run_experiment(N)\n",
    "    c+=ci\n",
    "    a+=ai\n",
    "\n",
    "print(c/RUNS)\n",
    "print(a/RUNS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.651\n",
      "3.019\n"
     ]
    }
   ],
   "source": [
    "RUNS = 1000\n",
    "N  = 100\n",
    "c = 0\n",
    "a = 0\n",
    "\n",
    "for i in range(RUNS):\n",
    "    ci, ai = run_experiment(N)\n",
    "    c+=ci\n",
    "    a+=ai\n",
    "\n",
    "print(c/RUNS)\n",
    "print(a/RUNS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "DIM = 2\n",
    "COLORS = ['red', 'blue']\n",
    "\n",
    "def plot_data_with_labels(x, y, ax):\n",
    "    unique = np.unique(y)\n",
    "    for li in range(len(unique)):\n",
    "        x_sub = x[y == unique[li]]\n",
    "        ax.scatter(x_sub[:, 0], x_sub[:, 1], c = COLORS[li])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# def plot_svm_separator(ax, w_svm_norm, bias_norm):\n",
    "#     slope = -w[0] / w[1]\n",
    "#     intercept = -b / w[1]\n",
    "#     x = np.arange(-1, 2)\n",
    "#     ax.plot(x, x * slope + intercept, 'k-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_plot_points_from_vector(vector):\n",
    "    x = np.array([-1, 1])\n",
    "    y = (- vector[1] * x - vector[0]) / vector[2]\n",
    "    return (x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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o39FGRwKAHEdZBQAXdDHuoroHd9fei3u1ZOASdavdzehIAGAXlFUAcDEHLx2U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\nKiIiIiKWpbAqIiIiIpb1fy4BelKVkR8yAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114564198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "# plot_separator(ax, w, 0)\n",
    "plot_data_with_labels(points, labels, ax)\n",
    "\n",
    "lx, ly  = get_plot_points_from_vector(fx_vector)\n",
    "ax.plot(lx, ly, 'g', lw=1)\n",
    "\n",
    "lx, ly  = get_plot_points_from_vector(w)\n",
    "ax.plot(lx, ly, 'b', lw=2)\n",
    "\n",
    "lx, ly  = get_plot_points_from_vector(w_s)\n",
    "ax.plot(lx, ly, 'r', lw=3)\n",
    "\n",
    "# show data and w\n",
    "plot_separator(ax, w_svm_norm, bias_norm)"
   ]
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}