Naive bayes explained.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from matplotlib import colors\n",
    "from sklearn.naive_bayes import GaussianNB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "mu1 = [1, 1]\n",
    "cov1 = 0.3 * np.eye(2)\n",
    "\n",
    "mu2 = [3, 2]\n",
    "#cov2 = np.eye(2) * np.array([0.4, 0.1])\n",
    "cov2 = np.eye(2) * 0.3\n",
    "\n",
    "X = np.concatenate([np.random.multivariate_normal(mu1, cov1, 20),\n",
    "                    np.random.multivariate_normal(mu2, cov2, 40)])\n",
    "y = np.zeros(60)\n",
    "y[20:] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "clf = GaussianNB()\n",
    "clf.fit(X, y)\n",
    "\n",
    "# predict the classification probabilities on a grid\n",
    "xlim = (-1, 5)\n",
    "ylim = (-1, 5)\n",
    "xx, yy = np.meshgrid(np.linspace(xlim[0], xlim[1], 71),\n",
    "                     np.linspace(ylim[0], ylim[1], 81))\n",
    "Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])\n",
    "Z = Z[:, 1].reshape(xx.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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PVBbQ1NbM2JTRxLou3/EtfrybyBjzM6ANmA00AKeAXCDRWvtu30sFY8yLwBlr7Q8usY3C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\nIsD/Bzu++I+TzriEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1c95f48550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "fox_colors=['#267f8c', '#7db686', '#abc433', '#d3d724']\n",
    "levels = [0, 1]\n",
    "cmap, norm = mpl.colors.from_levels_and_colors(levels=levels, colors=fox_colors[:2], extend='max')\n",
    "\n",
    "ax.scatter(X[:, 0], X[:, 1],  c=y ,cmap=cmap, norm=norm, zorder=2, edgecolors='none')\n",
    "\n",
    "#ax.contour(xx, yy, Z, [0.5], colors='k')\n",
    "\n",
    "ax.set_xlim(xlim)\n",
    "ax.set_ylim(ylim)\n",
    "\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "\n",
    "plt.savefig('graphs/nb/nb_demo.jpg', format='jpg', dpi=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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
}