lec20.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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy import random as rand\n",
    "from numpy import linalg as lin\n",
    "import random\n",
    "from cs771 import genSyntheticData as gsd\n",
    "from cs771 import plotData as pd\n",
    "from cs771 import utils\n",
    "from keras.datasets import mnist"
   ]
  },
  {
   "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": [
    "def doLSReg( X, y, weights = [] ):\n",
    "    # If no weights are specified, do usual least squares\n",
    "    if len(weights) == 0:\n",
    "        return 1/(np.sum( np.square( X ))) * X.dot( y )\n",
    "    # Else if weights are specified, solve the weighted least squares problem\n",
    "    else:\n",
    "        return 1/(weights.dot( np.square( X ))) * X.dot( np.multiply( weights, y ) )\n",
    "\n",
    "def doEStep( X, y, wVals ):\n",
    "    residuals = np.matmul( X[:,np.newaxis], wVals[np.newaxis,:] ) - y[:,np.newaxis]\n",
    "    qVals = np.exp( -np.square( residuals ) / 2 )\n",
    "    rowSum = qVals.sum( axis = 1 )\n",
    "    qVals = qVals / rowSum[:, np.newaxis]\n",
    "    return qVals\n",
    "\n",
    "def doMStep( X, y, qVals, C, prevWVals ):\n",
    "    wVals = np.zeros( prevWVals.shape )\n",
    "    \n",
    "    # Process every component\n",
    "    for c in range( C ):\n",
    "        # Get hold of the weights different data points have given to this component\n",
    "        q = qVals[:, c]\n",
    "        amountData = sum(q)\n",
    "        # If there is enough data for this component, do weighted least squares to get the weighted MLE\n",
    "        if amountData > 1:\n",
    "            wVals[c] = doLSReg( X, y, weights = q )\n",
    "        # If some cluster is almost empty, return the old value of the model for this component\n",
    "        else:\n",
    "            wVals[c] = prevWVals[c]\n",
    "    return wVals\n",
    "\n",
    "def doEMMR( X, y, C, init, niter ):\n",
    "    wVals = init\n",
    "    for t in range( niter ):\n",
    "        qVals = doEStep( X, y, wVals )\n",
    "        wVals = doMStep( X, y, qVals, C, wVals )\n",
    "    return (wVals, qVals)\n",
    "\n",
    "n = 40\n",
    "\n",
    "X = np.linspace( 0, 1, n, endpoint = True )\n",
    "wAst1 = 2\n",
    "wAst2 = 6\n",
    "noise = rand.normal( 0, 0.1, (n,) )\n",
    "y = np.zeros( X.shape )\n",
    "y[::2] = X[::2] * wAst1\n",
    "y[1::2] = X[1::2] * wAst2\n",
    "y = y + noise\n",
    "\n",
    "wHat = doLSReg( X, y )\n",
    "\n",
    "fig = pd.getFigure( 7, 7 )\n",
    "pd.plot2D( np.hstack( (X[:, np.newaxis], y[:, np.newaxis]) ), fig, color = 'b', marker = 'o', size = 20 )\n",
    "pd.plotLine( np.array( [wHat, -1] ) , 0, fig, color = 'y', linestyle = \"--\", xlimL = 0, xlimR = 1, label = \"Least Squares\" )\n",
    "\n",
    "# Careful initialization is required here, just as it was for (soft) k-means\n",
    "# If we initialize both models to be equal in the beginning, then the procedure cannot learn two components\n",
    "# Try setting, for example, init = np.array( [1,1] ) and see for yourself\n",
    "init = np.array( [0,0.5] )\n",
    "pd.plotLine( np.array( [init[0], -1] ) , 0, fig, color = 'k', linestyle = \":\", xlimL = 0, xlimR = 1, label = \"Initial w1\" )\n",
    "pd.plotLine( np.array( [init[1], -1] ) , 0, fig, color = 'k', linestyle = \":\", xlimL = 0, xlimR = 1, label = \"Initial w2\" )\n",
    "\n",
    "# The EM algorithm is very quick at identifying that there are two populations in the data\n",
    "# Within very few iterations, it converges to the two models\n",
    "C = 2\n",
    "niter = 5\n",
    "(wVals, qVals) = doEMMR( X, y, C, init, niter)\n",
    "\n",
    "pd.plotLine( np.array( [wVals[0], -1] ) , 0, fig, color = 'b', linestyle = \"-\", xlimL = 0, xlimR = 1, label = \"w1 after %s iter\" % niter )\n",
    "pd.plotLine( np.array( [wVals[1], -1] ) , 0, fig, color = 'b', linestyle = \"-\", xlimL = 0, xlimR = 1, label = \"w2 after %s iter\" % niter )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction Accuracy:  0.8573\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1296x4608 with 120 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Learn a single (general) Gaussian per class\n",
    "def learnClassConditionalDist( X, y ):\n",
    "    (labels, labelCounts) = np.unique( y, return_counts = True )\n",
    "    C = labels.size\n",
    "    (n, d) = X.shape\n",
    "    muVals = np.zeros( (C, d) )\n",
    "    SigmaVals = np.zeros( (C, d, d) )\n",
    "    for c in range( C ):\n",
    "        XThisLabel = X[y == c]\n",
    "        # MLE for mean is simply the empirical mean (aka sample mean) of feature vectors of this class\n",
    "        muVals[c] = np.mean( XThisLabel, axis = 0 )\n",
    "        XCent = XThisLabel - muVals[c]\n",
    "        # MLE for covariance matrix is simply the empirical/sample covariance matrix of this class\n",
    "        SigmaVals[c] = 1/labelCounts[c]*(XCent.T).dot( XCent )\n",
    "    return (C, list( zip( muVals, SigmaVals, np.arange( C ), labelCounts/n ) ))\n",
    "\n",
    "# Stretch out the 28 x 28 image into a 784 dimensional vector\n",
    "def flattenTensor( X ):\n",
    "    n = X.shape[0]\n",
    "    d = np.prod( X.shape[1:] )\n",
    "    return X.reshape( n, d )\n",
    "\n",
    "def predictClassScores( X, mu, Sigma, p, mask = [] ):\n",
    "    # If no mask was provided, then we need to consider all coordinates of the feature vector\n",
    "    if len(mask) == 0:\n",
    "        mask = np.ones( (X.shape[1],), dtype=bool )\n",
    "    \n",
    "    XCent = X[:,mask] - mu[mask]\n",
    "    # The covariance matrix will mostly be non-invertible in this case\n",
    "    # This is because some pixels are always white in every image i.e. zero variance\n",
    "    # The Moore-Penrose \"pseudoinverse\" is used in such situations\n",
    "    SInv = lin.pinv( Sigma[mask,:][:,mask] )\n",
    "    # numpy has a helpful routine that directly calculates the logdet of a matrix\n",
    "    # More numerically stable in several situations -- no exploding outputs\n",
    "    (sign, logdet) = lin.slogdet( Sigma[mask,:][:,mask] )\n",
    "    # sign = 0 is the routines way of telling us that the determinant was zero\n",
    "    # The determinant of a covariance matrix should always be non-negative\n",
    "    if sign <= 0:\n",
    "        SLogDet = 0\n",
    "    else:\n",
    "        SLogDet = logdet\n",
    "    # This term gives us (ignoring additive constants) ln P[x | y, \\theta]\n",
    "    term1 = 0.5 * (-SLogDet - np.sum( np.multiply( np.dot(XCent, SInv), XCent), axis = 1 ))\n",
    "    # This term gives us ln P[y | \\theta]\n",
    "    term2 = np.log( p )\n",
    "    return term1 + term2\n",
    "\n",
    "def predictGen( X, model, C, mask = [] ):\n",
    "    classScores = np.zeros( (X.shape[0], C) )\n",
    "    for mu, Sigma, c, p in model:\n",
    "        classScores[:,c] = predictClassScores( X, mu, Sigma, p, mask )\n",
    "    return np.argmax( classScores, axis = 1 )\n",
    "\n",
    "((XTrain, yTrain), (XTest, yTest)) = mnist.load_data()\n",
    "\n",
    "# Normalize data coordinates otherwise numbers in later calculations explode\n",
    "# Also, flatten images for sake of convenience\n",
    "imShape = XTrain.shape[1:]\n",
    "XTrainFlat = flattenTensor( XTrain/256 )\n",
    "XTestFlat = flattenTensor( XTest/256 )\n",
    "\n",
    "(C, model) = learnClassConditionalDist( XTrainFlat, yTrain )\n",
    "yPred = predictGen( XTestFlat, model, C )\n",
    "\n",
    "print( \"Prediction Accuracy: \", sum(yPred == yTest)/yTest.size )\n",
    "\n",
    "numRows = 20\n",
    "numCols = 6\n",
    "\n",
    "fig2, axs2 = pd.getFigList( numRows, numCols, sizey = 3.2 )\n",
    "labels = [\"True Label: %s\\nPred Label: %s\" % (yTest[i], yPred[i]) for i in range( numRows * numCols )]\n",
    "pd.showImagesNoAxes( axs2, XTestFlat[:numRows*numCols], numRows, numCols, resize = True, imShape = imShape, labelList = labels )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction Accuracy on Censored Images:  0.814\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1296x691.2 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1296x756 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You may yry more aggressive censoring e.g. X[:, 5:20, 5:20] = 0 which wipes out 25% of the pixels\n",
    "# Accuracy will fall as we wipe out more and more pixels\n",
    "def censorImages( X ):\n",
    "    # Wipe out 10% of the pixels from the central part of the image\n",
    "    X[:, 8:17, 8:17] = 0\n",
    "    return X\n",
    "\n",
    "# Warning: if we completely wipe out the images e.g. X[:, :, :] = 0, even then we will get ~11% accuracy\n",
    "# This is because the all white image gets classified as the digit 1 due to the image 1 being relatively\n",
    "# popular in the database as well as due to the digit 1 having the most number of white pixels anyway\n",
    "\n",
    "# Make sure that reconstructed image does not have any negative-valued pixels\n",
    "def truncatePixels( X, low = 0, high = 1 ):\n",
    "    X[X < low] = low\n",
    "    X[X > high] = high\n",
    "    return X\n",
    "\n",
    "# Reconstruct the image using the Gaussian conditionals\n",
    "def reconstructImages( X, yPred, model, mask ):\n",
    "    XRecon = np.zeros( X.shape )\n",
    "    # Pixels observed are used as is in the reconstruction\n",
    "    XRecon[:, mask] = X[:, mask]\n",
    "    for i in range( X.shape[0] ):\n",
    "        ( mu, Sigma, c, p ) = model[yPred[i]]\n",
    "        recon = mu[~mask] + Sigma[~mask,:][:,mask].dot( lin.pinv( Sigma[mask,:][:,mask] ).dot( (XRecon[i,mask] - mu[mask]) ) )\n",
    "        XRecon[i, ~mask] = recon\n",
    "    return truncatePixels( XRecon )\n",
    "\n",
    "XTestCensorFlat = flattenTensor( censorImages( XTest ) / 256 )\n",
    "mask = flattenTensor( censorImages( np.ones( imShape )[np.newaxis, :] ) )[0] == 1\n",
    "\n",
    "yPred = predictGen( XTestCensorFlat, model, C, mask )\n",
    "\n",
    "print( \"Prediction Accuracy on Censored Images: \", sum(yPred == yTest)/yTest.size )\n",
    "\n",
    "numRows = 3\n",
    "numCols = 6\n",
    "\n",
    "XTestReconFlat = reconstructImages( XTestCensorFlat[:numRows*numCols], yPred[:numRows*numCols], model, mask )\n",
    "\n",
    "fig3, axs3 = pd.getFigList( numRows, numCols, sizey = 3.2 )\n",
    "labels = [\"True Label: %s\\nCensored Image\" % yTest[i] for i in range( numRows * numCols )]\n",
    "pd.showImagesNoAxes( axs3, XTestCensorFlat[:numRows*numCols], numRows, numCols, resize = True, imShape = imShape, labelList = labels )\n",
    "\n",
    "fig4, axs4 = pd.getFigList( numRows, numCols, sizey = 3.5 )\n",
    "labels = [\"True Label: %s\\nPred Label: %s\\nReconstructed Image\" % (yTest[i], yPred[i]) for i in range( numRows * numCols )]\n",
    "pd.showImagesNoAxes( axs4, XTestReconFlat[:numRows*numCols], numRows, numCols, resize = True, imShape = imShape, labelList = labels )"
   ]
  }
 ],
 "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
}