multiclass_classifier.ipynb

{
 "cells": [
  {
   "cell_type": "heading",
   "metadata": {
    "collapsed": true
   },
   "level": 1,
   "source": [
    "Bayesian Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n  %reload_ext autoreload\n1.1.2\n1.0.0\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 1\n",
    "\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.cross_validation import train_test_split\n",
    "import numpy as np\n",
    "%aimport tensorflow\n",
    "import tensorflow as tf\n",
    "\n",
    "import edward as ed\n",
    "from edward.models import Normal, Bernoulli, Categorical\n",
    "# from tensorflow.contrib.distributions import Categorical\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_style(\"darkgrid\")\n",
    "%matplotlib inline\n",
    "\n",
    "tf.logging.set_verbosity(tf.logging.ERROR)\n",
    "\n",
    "print(ed.__version__)\n",
    "print(tf.__version__)"
   ]
  },
  {
   "cell_type": "heading",
   "metadata": {},
   "level": 1,
   "source": [
    "Load in iris data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = load_iris()\n",
    "X = iris.data[:, :2].astype(np.float32)\n",
    "Y = iris.target.astype(np.int32)\n",
    "C = len(iris.target_names)\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=.5)"
   ]
  },
  {
   "cell_type": "heading",
   "metadata": {},
   "level": 2,
   "source": [
    "Binary Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BinaryModel(object):\n",
    "    def __init__(self, N, D):\n",
    "        self.X = tf.placeholder(tf.float32, shape=[N, D])\n",
    "        self.w = Normal(mu=tf.zeros([D]), sigma=tf.ones([D]))\n",
    "        self.b = Normal(mu=tf.zeros([1]), sigma=tf.ones([1]))\n",
    "        self.s = Normal(mu=ed.dot(self.X, self.w) + self.b, sigma=tf.ones(N))\n",
    "        self.qw = Normal(mu=tf.Variable(tf.random_normal([D])), sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D]))))\n",
    "        self.qb = Normal(mu=tf.Variable(tf.random_normal([1])), sigma=tf.nn.softplus(tf.Variable(tf.random_normal([1]))))\n",
    "        self.y = Bernoulli(logits=self.s)\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        y = (y > 0).astype(np.int32)\n",
    "        # inference = ed.MFVI({self.w: self.qw, self.b: self.qb}, data={self.X: X, self.y: y})\n",
    "        # inference.run()\n",
    "        inference = ed.Inference({self.w: self.qw, self.b: self.qb}, data={self.X: X, self.y: y})\n",
    "        sess = ed.get_session()\n",
    "        init = tf.global_variables_initializer()\n",
    "        init.run()\n",
    "        \n",
    "    def predict_proba(self, X, y=None):\n",
    "        y_post = ed.copy(self.y, {self.X: X, self.w: self.qw, self.b: self.qb})\n",
    "        sess = ed.get_session()\n",
    "        y_hat = sess.run(y_post.mean())\n",
    "        return y_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  5.82982844e-04,   3.83698428e-03,   5.64901298e-03,\n         2.89702602e-03,   3.82500514e-03,   1.85881509e-03,\n         5.95472578e-04,   1.89975109e-02,   1.63579807e-02,\n         2.39507407e-02,   4.53087091e-02,   4.32373350e-03,\n         9.07501113e-03,   6.99760672e-03,   1.39794650e-03,\n         1.24007941e-03,   1.56162726e-03,   3.78996687e-04,\n         1.39530760e-03,   5.75790706e-04,   5.66998078e-03,\n         8.84821755e-04,   1.64044928e-03,   4.69403400e-04,\n         2.98791099e-04,   1.19498959e-02,   7.42657576e-04,\n         6.57544378e-03,   5.59139624e-03,   1.61973678e-03,\n         2.72609969e-03,   2.59756949e-03,   1.22905697e-03,\n         1.33835971e-02,   1.59463802e-04,   8.38618074e-03,\n         6.97880844e-03,   1.59374147e-03,   2.97951954e-03,\n         1.22631118e-02,   1.34459755e-04,   6.52364906e-05,\n         5.17150213e-04,   7.69510749e-04,   6.89820386e-03,\n         3.71592119e-03,   1.36271864e-02,   2.25982582e-03,\n         7.75552064e-04,   5.24027200e-05,   4.36697202e-03,\n         3.59795056e-03,   1.71522304e-04,   7.60399969e-04,\n         1.00311256e-04,   1.83182550e-04,   2.59484106e-04,\n         1.31524680e-03,   1.61872897e-02,   2.25747150e-04,\n         3.46563105e-03,   4.50058113e-04,   1.67189617e-04,\n         1.85891346e-03,   1.36320450e-04,   5.05121909e-02,\n         9.63556301e-03,   3.87062086e-04,   6.80046331e-04,\n         4.73646796e-04,   1.91664174e-02,   1.63171469e-04,\n         1.16417406e-03,   1.13019848e-03,   3.31527889e-02], dtype=float32)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = BinaryModel(*X_train.shape)\n",
    "model.fit(X_train, Y_train)\n",
    "model.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "heading",
   "metadata": {},
   "level": 2,
   "source": [
    "Multiclass Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MulticlassModel(object):\n",
    "    def __init__(self, N, D, C):\n",
    "        self.X = tf.placeholder(tf.float32, shape=[N, D])\n",
    "        self.w = Normal(mu=tf.zeros([D, C]), sigma=tf.ones([D, C]))\n",
    "        self.b = Normal(mu=tf.zeros([C]), sigma=tf.ones([C]))\n",
    "        self.s = Normal(mu=tf.matmul(self.X, self.w) + self.b, sigma=tf.ones([N, C]))\n",
    "        self.qw = Normal(mu=tf.Variable(tf.random_normal([D, C])), sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D, C]))))\n",
    "        self.qb = Normal(mu=tf.Variable(tf.random_normal([C])), sigma=tf.nn.softplus(tf.Variable(tf.random_normal([C]))))\n",
    "        self.y = Categorical(logits=tf.nn.softmax(logits=self.s))\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        # inference = ed.MFVI({self.w: self.qw, self.b: self.qb}, data={self.X: X, self.y: y})\n",
    "        # inference.run()\n",
    "        inference = ed.Inference({self.w: self.qw, self.b: self.qb}, data={self.X: X, self.y: y})\n",
    "        sess = ed.get_session()\n",
    "        init = tf.global_variables_initializer()\n",
    "        init.run()\n",
    "        \n",
    "    def predict_proba(self, X, y=None):\n",
    "        y_post = ed.copy(self.y, {self.X: X, self.w: self.qw, self.b: self.qb})\n",
    "        sess = ed.get_session()\n",
    "        y_hat = sess.run(y_post.mean())\n",
    "        print(y_hat)\n",
    "        return y_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "mean is not implemented",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-10-841ad782b0f3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mMulticlassModel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX_train\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict_proba\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_test\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-8-ab6ee2527c2c>\u001b[0m in \u001b[0;36mpredict_proba\u001b[0;34m(self, X, y)\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0my_post\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0med\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mqw\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mqb\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m         \u001b[0msess\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0med\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_session\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m         \u001b[0my_hat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msess\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_post\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m         \u001b[0;32mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_hat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0my_hat\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python2.7/site-packages/edward/models/random_variable.pyc\u001b[0m in \u001b[0;36mmean\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    112\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    113\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 114\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistribution\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    115\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    116\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mvariance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python2.7/site-packages/tensorflow/contrib/distributions/python/ops/distribution.pyc\u001b[0m in \u001b[0;36mmean\u001b[0;34m(self, name)\u001b[0m\n\u001b[1;32m    784\u001b[0m     \u001b[0;34m\"\"\"Mean.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    785\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_name_scope\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 786\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_mean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    787\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    788\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0m_variance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python2.7/site-packages/tensorflow/contrib/distributions/python/ops/distribution.pyc\u001b[0m in \u001b[0;36m_mean\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    779\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    780\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0m_mean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 781\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"mean is not implemented\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    782\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    783\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"mean\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: mean is not implemented"
     ],
     "output_type": "error"
    }
   ],
   "source": [
    "Y_train = Y_train.astype(np.float32)\n",
    "model = MulticlassModel(X_train.shape[0], X_train.shape[1], C)\n",
    "model.fit(X_train, Y_train)\n",
    "model.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H/YuLo1uK2S0mPmjo5/qaxG8cLBJn3IBdX1/P3/7t33Lw4EG+8pWv8Mtf/lJ2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\n+pCDChwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1155091d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logreg = LogisticRegression(C=1e5)\n",
    "\n",
    "# we create an instance of Logistic Regression Classifier and fit the data.\n",
    "logreg.fit(X, Y)\n",
    "\n",
    "h = .02  # step size in the mesh\n",
    "\n",
    "# Plot the decision boundary. For that, we will assign a color to each\n",
    "# point in the mesh [x_min, x_max]x[y_min, y_max].\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "Z = logreg.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "# Put the result into a color plot\n",
    "Z = Z.reshape(xx.shape)\n",
    "plt.figure(1, figsize=(6, 6), facecolor='w')\n",
    "plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)\n",
    "\n",
    "# Plot also the training points\n",
    "plt.scatter(X[:, 0], X[:, 1], c=Y, edgecolors='k', cmap=plt.cm.Paired)\n",
    "plt.xlabel('Sepal length')\n",
    "plt.ylabel('Sepal width')\n",
    "plt.xlim(xx.min(), xx.max())\n",
    "plt.ylim(yy.min(), yy.max())\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    ""
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2.0
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}