Bayesian_Gaussian_GMM_Demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Adapted from: https://github.com/lazyprogrammer/machine_learning_examples/blob/master/unsupervised_class3/\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import multivariate_normal as mvn\n",
    "import pandas as pd\n",
    "import scipy.misc\n",
    "from sklearn.utils import shuffle\n",
    "from sklearn.mixture import BayesianGaussianMixture\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def clamp_sample(x):\n",
    "  x = np.minimum(x, 1)\n",
    "  x = np.maximum(x, 0)\n",
    "  return x\n",
    "\n",
    "def get_mnist(limit=None):\n",
    "  print(\"Reading in and transforming data...\")\n",
    "  df = pd.read_csv('large_files/train.csv')\n",
    "  data = df.values\n",
    "  # np.random.shuffle(data)\n",
    "  X = data[:, 1:] / 255.0 # data is from 0..255\n",
    "  Y = data[:, 0]\n",
    "  X, Y = shuffle(X, Y)\n",
    "  if limit is not None:\n",
    "    X, Y = X[:limit], Y[:limit]\n",
    "  return X, Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BayesClassifier:\n",
    "  def fit(self, X, Y):\n",
    "    # assume classes are numbered 0...K-1\n",
    "    self.K = len(set(Y))\n",
    "\n",
    "    self.gaussians = []\n",
    "    self.p_y = np.zeros(self.K)\n",
    "    for k in range(self.K):\n",
    "      print(\"Fitting gmm\", k)\n",
    "      Xk = X[Y == k]\n",
    "      self.p_y[k] = len(Xk)\n",
    "      gmm = BayesianGaussianMixture(10)\n",
    "      gmm.fit(Xk)\n",
    "      self.gaussians.append(gmm)\n",
    "    # normalize p(y)\n",
    "    self.p_y /= self.p_y.sum()\n",
    "\n",
    "  def sample_given_y(self, y):\n",
    "    gmm = self.gaussians[y]\n",
    "    sample = gmm.sample()\n",
    "    # note: sample returns a tuple containing 2 things:\n",
    "    # 1) the sample\n",
    "    # 2) which cluster it came from\n",
    "    # we'll use (2) to obtain the means so we can plot\n",
    "    # them like we did in the previous script\n",
    "    # we cheat by looking at \"non-public\" params in\n",
    "    # the sklearn source code\n",
    "    mean = gmm.means_[sample[1]]\n",
    "    return clamp_sample( sample[0].reshape(28, 28) ), mean.reshape(28, 28)\n",
    "\n",
    "  def sample(self):\n",
    "    y = np.random.choice(self.K, p=self.p_y)\n",
    "    return clamp_sample( self.sample_given_y(y) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading in and transforming data...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 3\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 4\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 5\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 6\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 7\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 8\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting gmm 9\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if __name__ == '__main__':\n",
    "  X, Y = get_mnist()\n",
    "  clf = BayesClassifier()\n",
    "  clf.fit(X, Y)\n",
    "\n",
    "  for k in range(clf.K):\n",
    "    # show one sample for each class\n",
    "    # also show the mean image learned\n",
    "\n",
    "    sample, mean = clf.sample_given_y(k)\n",
    "\n",
    "    plt.subplot(1,2,1)\n",
    "    plt.imshow(sample, cmap='gray')\n",
    "    plt.title(\"Sample\")\n",
    "    plt.subplot(1,2,2)\n",
    "    plt.imshow(mean, cmap='gray')\n",
    "    plt.title(\"Mean\")\n",
    "    plt.show()\n",
    "\n",
    "  # generate a random sample\n",
    "  sample, mean = clf.sample()\n",
    "  plt.subplot(1,2,1)\n",
    "  plt.imshow(sample, cmap='gray')\n",
    "  plt.title(\"Random Sample from Random Class\")\n",
    "  plt.subplot(1,2,2)\n",
    "  plt.imshow(mean, cmap='gray')\n",
    "  plt.title(\"Corresponding Cluster Mean\")\n",
    "  plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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