lec16.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import random as rand\n",
    "from cs771 import genSyntheticData as gsd\n",
    "from cs771 import plotData as pd\n",
    "from cs771 import utils\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# True Gaussian distribution from which data is generated\n",
    "muAst = 3\n",
    "sigmaAst = 2\n",
    "\n",
    "# Number of samples\n",
    "n = 10\n",
    "\n",
    "# Get samples\n",
    "X = rand.normal( muAst, sigmaAst, n )\n",
    "\n",
    "# Make samples into 2D points so that they can be plotted\n",
    "X2D = np.ones( (n, 2) ) * -0.1\n",
    "X2D[:,0] = X\n",
    "\n",
    "# A global variable (sorry - I know global vars are bad) to plot the MAP estimate\n",
    "mode = 0\n",
    "\n",
    "def getPDFGaussian( X ):\n",
    "    global sigma, mu\n",
    "    return 1/np.sqrt( 2 * np.pi * np.square(sigma) ) * np.exp( -np.square( X - mu )/(2 * np.square( sigma )) )\n",
    "\n",
    "def getPDFUniform( X ):\n",
    "    global a, b\n",
    "    pdf = np.ones( X.shape ) * 1/(b - a)\n",
    "    pdf[X < a] = 0\n",
    "    pdf[X > b] = 0\n",
    "    return pdf\n",
    "\n",
    "def getPosterior( W ):\n",
    "    global mode, priorPDF, X\n",
    "    prior = priorPDF( W )\n",
    "    temp = utils.getAllPairsDistances( W[:, np.newaxis], X[:, np.newaxis] )\n",
    "    likelihood = np.prod( np.exp(-temp/(2 * np.square( sigmaAst ))), axis = 1)\n",
    "    posterior = np.multiply( prior, likelihood )\n",
    "    # It is tedious to do the exact integration so we normalize the crude way\n",
    "    posterior = posterior/np.sum( posterior )\n",
    "    # Set the mode variable so that we may plot it outside\n",
    "    mode = W[np.argmax( posterior )]\n",
    "    return posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Uniform Prior\n",
    "a = 0\n",
    "b = 2\n",
    "\n",
    "nBins = 100\n",
    "priorPDF = getPDFUniform\n",
    "\n",
    "mu = muAst\n",
    "sigma = sigmaAst\n",
    "\n",
    "# We will notice that since the prior excludes the true muAst, the MAP procedure will\n",
    "# instead offer the model most suitable within the support of the prior (at one extreme)\n",
    "# end of the support of the prior. On the other hand, if we set the support to be something\n",
    "# like a = 4, b = 6, then you will find MAP latching on to the other extreme end of the support\n",
    "# The is no accident -- the MAP does indeed compute a constrained optimization problem in this case\n",
    "\n",
    "# However, if we use a less restrictive prior that does include the true muAst, for example\n",
    "# a = -5, b = 5, then the MAP procedure, when given enough data points (say set n = 200 or so)\n",
    "# will recover muAst very faithfully\n",
    "fig = pd.getFigure( 7, 7 )\n",
    "pd.plotCurve( getPDFGaussian, fig, mode = \"batch\", color = 'k', linestyle = ':', xlimL = -3, xlimR = 7, nBins = nBins, label = \"True Distribution\" )\n",
    "pd.plot2D( X2D, fig, color = 'g', marker = 'x', size = 100 )\n",
    "pd.plotCurve( getPDFUniform, fig, mode = \"batch\", color = 'y', linestyle = ':', xlimL = -3, xlimR = 7, nBins = nBins, label = \"Prior\" )\n",
    "pd.plotCurve( getPosterior, fig, mode = \"batch\", color = 'b', linestyle = '-', xlimL = -3, xlimR = 7, nBins = nBins, label = \"Posterior\" )\n",
    "pd.plotVerticalLine( mode, fig, color = 'm', linestyle = '-', yLimB = 0, yLimT = 1, nBins = nBins, label = \"MAP\")\n",
    "plt.ylim( top = 1.0 )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = muAst\n",
    "sigma = sigmaAst\n",
    "\n",
    "fig2 = pd.getFigure( 7, 7 )\n",
    "pd.plotCurve( getPDFGaussian, fig2, mode = \"batch\", color = 'k', linestyle = ':', xlimL = -3, xlimR = 7, nBins = nBins, label = \"True Distribution\" )\n",
    "pd.plot2D( X2D, fig2, color = 'g', marker = 'x', size = 100 )\n",
    "\n",
    "# Let us instead use a Gaussian prior\n",
    "muPrior = -2\n",
    "sigmaPrior = 1\n",
    "\n",
    "mu = muPrior\n",
    "sigma = sigmaPrior\n",
    "priorPDF = getPDFGaussian\n",
    "\n",
    "# Notice that the posterior distribution also looks suspiciously Gaussian in this case.\n",
    "# Try changing the parameters of the prior and confirm that the posterior continues to\n",
    "# look like a Gaussian. This is again no accident -- the posterior is actually a Gaussian.\n",
    "# If our prior and likelihood distributions are both Gaussian then the posterior distribution\n",
    "# will also be Gaussian -- this is due to a beautiful phenonmenon called conjugacy which\n",
    "# we will briefly look in this course very soon -- more details in advanced courses like CS772\n",
    "pd.plotCurve( getPDFGaussian, fig2, mode = \"batch\", color = 'y', linestyle = ':', xlimL = -3, xlimR = 7, nBins = nBins, label = \"Prior\" )\n",
    "pd.plotCurve( getPosterior, fig2, mode = \"batch\", color = 'b', linestyle = '-', xlimL = -3, xlimR = 7, nBins = nBins, label = \"Posterior\" )\n",
    "pd.plotVerticalLine( mode, fig2, color = 'm', linestyle = '-', yLimB = 0, yLimT = 1, nBins = nBins, label = \"MAP\")\n",
    "plt.ylim( top = 1.0 )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "author": {
   "email": "purushot@cse.iitk.ac.in",
   "institution": "IIT Kanpur",
   "name": "Puru"
  },
  "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
}