Edward Bayesian Network Binary Classification Example.ipynb

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   "source": [
    "#!/usr/bin/env python\n",
    "\"\"\"\n",
    "Bayesian neural network for binary classification using mean-field variational inference.\n",
    "(see, e.g., Blundell et al. (2015); Kucukelbir et al. (2016))\n",
    "Inspired by autograd's Bayesian neural network example.\n",
    "\n",
    "Probability model:\n",
    "    Bayesian neural network\n",
    "    Prior: Normal\n",
    "    Likelihood: Bernoulli parameterized by fully connected NN\n",
    "Variational model\n",
    "    Likelihood: Mean-field Normal\n",
    "\"\"\"\n",
    "import edward as ed\n",
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "import pprint\n",
    "from random import shuffle\n",
    "\n",
    "from edward.models import Variational, Normal\n",
    "from edward.stats import norm,bernoulli, beta\n",
    "from edward.util import rbf\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_style('white')\n",
    "\n",
    "from sklearn import datasets\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn.datasets import make_moons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Rotate the samples just for fun\n",
    "angle = 45.\n",
    "theta = (angle/180.) * np.pi\n",
    "\n",
    "rotMatrix = np.array([[np.cos(theta), -np.sin(theta)], \n",
    "                         [np.sin(theta),  np.cos(theta)]])\n",
    "\n",
    "X, Y = make_moons(noise=0.2, random_state=0, n_samples=1000)\n",
    "\n",
    "X = scale(np.matmul(rotMatrix,X.T).T)\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=.15)\n",
    "\n",
    "\n",
    "train_data = tf.constant(np.column_stack((Y_train, X_train)),dtype=tf.float32)\n",
    "test_data = tf.constant(np.column_stack((Y_test, X_test)),dtype=tf.float32)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   "source": [
    "class BayesianNN:\n",
    "    \"\"\"\n",
    "    Bayesian neural network for regressing outputs y on inputs x.\n",
    "\n",
    "    p((x,y), z) = Normal(y | NN(x; z), lik_variance) *\n",
    "                  Normal(z | 0, prior_variance),\n",
    "\n",
    "    where z are neural network weights, and with known lik_variance\n",
    "    and prior_variance.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    layer_sizes : list\n",
    "        The size of each layer, ordered from input to output.\n",
    "    nonlinearity : function, optional\n",
    "        Non-linearity after each linear transformation in the neural\n",
    "        network; aka activation function.\n",
    "    lik_variance : float, optional\n",
    "        Variance of the normal likelihood; aka noise parameter,\n",
    "        homoscedastic variance, scale parameter.\n",
    "    prior_variance : float, optional\n",
    "        Variance of the normal prior on weights; aka L2\n",
    "        regularization parameter, ridge penalty, scale parameter.\n",
    "    \"\"\"\n",
    "    def __init__(self, layer_sizes, nonlinearity=tf.nn.tanh,\n",
    "        lik_variance=0.01, prior_variance=0.001):\n",
    "        self.layer_sizes = layer_sizes\n",
    "        self.nonlinearity = nonlinearity\n",
    "        self.lik_variance = lik_variance\n",
    "        self.prior_variance = prior_variance\n",
    "\n",
    "        self.num_layers = len(layer_sizes)\n",
    "        self.weight_dims = list(zip(layer_sizes[:-1], layer_sizes[1:]))\n",
    "        self.num_vars = sum((m+1)*n for m, n in self.weight_dims)\n",
    "\n",
    "    def unpack_weights(self, z):\n",
    "        \"\"\"Unpack weight matrices and biases from a flattened vector.\"\"\"\n",
    "        for m, n in self.weight_dims:\n",
    "            yield tf.reshape(z[:m*n],        [m, n]), \\\n",
    "                  tf.reshape(z[m*n:(m*n+n)], [1, n])\n",
    "            z = z[(m+1)*n:]\n",
    "\n",
    "    def mapping(self, x, z):\n",
    "        \"\"\"\n",
    "        mu = NN(x; z)\n",
    "\n",
    "        Note this is one sample of z at a time.\n",
    "\n",
    "        Parameters\n",
    "        -------\n",
    "        x : tf.tensor\n",
    "            n_data x D\n",
    "\n",
    "        z : tf.tensor\n",
    "            num_vars\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        tf.tensor\n",
    "            vector of length n_data\n",
    "        \"\"\"\n",
    "        h = x\n",
    "        for W, b in self.unpack_weights(z):\n",
    "            # broadcasting to do (h*W) + b (e.g. 40x10 + 1x10)\n",
    "            h = self.nonlinearity(tf.matmul(h, W) + b)\n",
    "\n",
    "        h = tf.squeeze(tf.sigmoid(h)) # n_data x 1 to n_data\n",
    "        return h\n",
    "\n",
    "    def log_prob(self, xs, zs):\n",
    "        \"\"\"Returns a vector [log p(xs, zs[1,:]), ..., log p(xs, zs[S,:])].\"\"\"\n",
    "        # Data must have labels in the first column and features in\n",
    "        # subsequent columns.\n",
    "        y = xs[:, 0]\n",
    "        x = xs[:, 1:]        \n",
    "        \n",
    "        log_prior = -self.prior_variance * tf.reduce_sum(zs*zs, 1)\n",
    "        ps = tf.pack([self.mapping(x, z) for z in tf.unpack(zs)])\n",
    "        \n",
    "        log_lik = -tf.reduce_sum((bernoulli.logpmf(1-y, p=ps)))/ self.lik_variance\n",
    "        return log_lik + log_prior\n",
    "      \n",
    "ed.set_seed(42)\n",
    "model = BayesianNN(layer_sizes=[2, 5, 5, 1], nonlinearity=tf.nn.tanh)\n",
    "variational = Variational()\n",
    "variational.add(Normal(model.num_vars))\n",
    "#data = build_toy_dataset()"
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
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   "source": [
    "# Helper function for creating data batches\n",
    "def chunks(l, n):\n",
    "    \"\"\"Yield successive n-sized chunks from l.\"\"\"\n",
    "    for i in range(0, len(l), n):\n",
    "        yield l[i:i+n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sess = ed.get_session()\n",
    "\n",
    "batch_size = 100\n",
    "batch_list = list(chunks(list(range(0, X_train.shape[0])), batch_size))\n",
    "batches_num = int(X_train.shape[0] / batch_size)\n",
    "idx = list(range(X_train.shape[0]))\n",
    "x = tf.placeholder(tf.float32, [batch_size,3])\n",
    "data = ed.Data(x)\n",
    "inference = ed.MFVI(model, variational, data)\n",
    "inference.initialize(n_print=10)"
   ]
  },
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   "source": [
    "for t in range(200):\n",
    "    avg_loss = 0.0\n",
    "    shuffle(idx)\n",
    "    X_train_shuffle = X_train[idx,:]\n",
    "    Y_train_shuffle = Y_train[idx]\n",
    "    for n in range(batches_num):\n",
    "        \n",
    "        train_batch = (np.column_stack((Y_train_shuffle[batch_list[n]], X_train_shuffle[batch_list[n],:])))\n",
    "        _, loss = sess.run([inference.train, inference.loss],\n",
    "                           feed_dict={x: train_batch})\n",
    "        avg_loss += loss\n",
    "        \n",
    "    avg_loss = avg_loss / batches_num\n",
    "    # Print a lower bound to the average marginal likelihood for an\n",
    "    # image.\n",
    "    print(\"avg. loss {:0.3f}\".format(avg_loss))\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Sample variational parameters\n",
    "mean, std = sess.run([variational.layers[0].m,\n",
    "                              variational.layers[0].s])\n",
    "rs = np.random.RandomState(0)\n",
    "zs = rs.randn(50, variational.num_vars) * std + mean\n",
    "zs = tf.constant(zs, dtype=tf.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "p = tf.pack([model.mapping(tf.constant(X_test,dtype=tf.float32), z) for z in tf.unpack(zs)])\n",
    "pred = np.squeeze(p.eval().mean(axis=0) >= 0.5)\n",
    "wrong_pred_0 = np.where(np.logical_and(np.squeeze(Y_test)!= pred, np.squeeze(Y_test) == 0))\n",
    "wrong_pred_1 = np.where(np.logical_and(np.squeeze(Y_test)!= pred, np.squeeze(Y_test) == 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
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   "outputs": [
    {
     "data": {
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oNSUinab0UY5pCw0R6TSNFBIwOrqZpUvXxCmjrSxbdhy9vbM7fhxtoSEinaag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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12fec2cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n",
    "ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
    "ax.scatter(X_test[wrong_pred_1, 0], X_test[wrong_pred_1, 1], color='m')\n",
    "ax.scatter(X_test[wrong_pred_0, 0], X_test[wrong_pred_0, 1], color='g')\n",
    "sns.despine()\n",
    "ax.set(title='Predicted labels in testing set', xlabel='X', ylabel='Y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tCgqcdNSKLqJL6GslYKRuotBbOFk8907BegSYTVXVetckqPgcmoD1rFvXTnb2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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12feb7d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X[Y==0, 0], X[Y==0, 1], label='Class 0')\n",
    "ax.scatter(X[Y==1, 0], X[Y==1, 1], color='r', label='Class 1')\n",
    "sns.despine(); ax.legend()\n",
    "ax.set(xlabel='X', ylabel='Y', title='Toy binary classification data set');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "grid = np.mgrid[-3:3:100j,-3:3:100j]\n",
    "grid_2d = grid.reshape(2, -1).T           \n",
    "\n",
    "pX = tf.pack([model.mapping(tf.constant(X,dtype=tf.float32), z) for z in tf.unpack(zs)])\n",
    "pred_X = np.squeeze(pX.eval().mean(axis=0) >= 0.5)              \n",
    "\n",
    "    \n",
    "p = tf.pack([model.mapping(tf.constant(grid_2d,dtype=tf.float32), z) for z in tf.unpack(zs)])\n",
    "pred_grid = np.squeeze(p.eval().mean(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LC5SQUmqt1vplKMxAy5ZZU0AEkSDgfgCf4kxyiOd29VckbOoZZXI/rFti/bxm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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x134da4f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "#grid = np.mgrid[100:-3:-3j,-3:3:100j]\n",
    "dummy_out = np.ones(grid.shape[1], dtype=np.int8)\n",
    "cmap = sns.diverging_palette(250, 12, s=85, l=25, as_cmap=True)\n",
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "contour = ax.contourf(*grid, pred_grid.reshape(100, 100), cmap=cmap)\n",
    "#ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1])\n",
    "#ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
    "ax.scatter(X[pred_X==0, 0], X[pred_X==0, 1], label='Class 0')\n",
    "ax.scatter(X[pred_X==1, 0], X[pred_X==1, 1], color='r', label='Class 1')\n",
    "cbar = plt.colorbar(contour, ax=ax)\n",
    "_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel='X', ylabel='Y');\n",
    "cbar.ax.set_ylabel('Posterior predictive mean probability of class label = 0');"
   ]
  }
 ],
 "metadata": {
  "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}