ML0120EN-4.1-Review-RBMMNIST.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src=\"https://ibm.box.com/shared/static/qo20b88v1hbjztubt06609ovs85q8fau.png\" width=\"400px\" align=\"center\"></a>\n",
    "\n",
    "<h1 align=\"center\"><font size=\"5\">RESTRICTED BOLTZMANN MACHINES</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Introduction</h3>\n",
    "<b>Restricted Boltzmann Machine (RBM):</b>  RBMs are shallow neural nets that learn to reconstruct data by themselves in an unsupervised fashion.  \n",
    "\n",
    "\n",
    "<h4>Why are RBMs important?</h4>\n",
    "It can automatically extract <b>meaningful</b> features from a given input.\n",
    "\n",
    "\n",
    "<h4>How does it work?</h4>\n",
    "RBM is a 2 layer neural network. Simply, RBM takes the inputs and translates those into a set of binary values that represents them in the hidden layer. Then, these numbers can be translated back to reconstruct the inputs. Through several forward and backward passes, the RBM will be trained, and a trained RBM can reveal which features are the most important ones when detecting patterns.   \n",
    "\n",
    "\n",
    "<h4>What are the applications of RBM?</h4>\n",
    "RBM is useful for <a href='http://www.cs.utoronto.ca/~hinton/absps/netflixICML.pdf'>  Collaborative Filtering</a>, dimensionality reduction, classification, regression, feature learning, topic modeling and even <b>Deep Belief Networks</b>.\n",
    "\n",
    "\n",
    "\n",
    "<h4>Is RBM a generative or Discriminative model?</h4>\n",
    "RBM is a generative model. Let me explain it by first, see what is different between discriminative and generative models: \n",
    "\n",
    "<b>Discriminative:</b> Consider a classification problem in which we want to learn to distinguish between Sedan cars (y = 1) and SUV cars (y = 0), based on some features of cars. Given a training set, an algorithm like logistic regression tries to find a straight line—that is, a decision boundary—that separates the suv and sedan.  \n",
    "<b>Generative:</b> looking at cars, we can build a model of what Sedan cars look like. Then, looking at SUVs, we can build a separate model of what SUV cars look like. Finally, to classify a new car, we can match the new car against the Sedan model, and match it against the SUV model, to see whether the new car looks more like the SUV or Sedan. \n",
    "\n",
    "Generative Models specify a probability distribution over a dataset of input vectors. We can do both supervise and unsupervised tasks with generative models:\n",
    "<ul>\n",
    "    <li>In an unsupervised task, we try to form a model for P(x), where P is the probability given x as an input vector.</li>\n",
    "    <li>In the supervised task, we first form a model for P(x|y), where P is the probability of x given y(the label for x). For example, if y = 0 indicates whether a car is a SUV or y = 1 indicates indicate a car is a Sedan, then p(x|y = 0) models the distribution of SUVs’ features, and p(x|y = 1) models the distribution of Sedans’ features. If we manage to find P(x|y) and P(y), then we can use <code>Bayes rule</code> to estimate P(y|x), because: $$p(y|x) = \\frac{p(x|y)p(y)}{p(x)}$$</li>\n",
    "</ul>\n",
    "Now the question is, can we build a generative model, and then use it to create synthetic data by directly sampling from the modeled probability distributions? Lets see. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of Contents</h2>\n",
    "<ol>\n",
    "    <li><a href=\"#ref1\">Initialization</a></li>\n",
    "    <li><a href=\"#ref2\">RBM layers</a></li>\n",
    "    <li><a href=\"#ref3\">What RBM can do after training?</a></li>\n",
    "    <li><a href=\"#ref4\">How to train the model?</a></li>\n",
    "    <li><a href=\"#ref5\">Learned features</a></li>\n",
    "</ol>\n",
    "<p></p>\n",
    "</div>\n",
    "<br>\n",
    "\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref1\"></a>\n",
    "<h3>Initialization</h3>\n",
    "\n",
    "First we have to load the utility file which contains different utility functions that are not connected\n",
    "in any way to the networks presented in the tutorials, but rather help in\n",
    "processing the outputs into a more understandable way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import urllib.request\n",
    "with urllib.request.urlopen(\"http://deeplearning.net/tutorial/code/utils.py\") as url:\n",
    "    response = url.read()\n",
    "target = open('utils.py', 'w')\n",
    "target.write(response.decode('utf-8'))\n",
    "target.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we load in all the packages that we use to create the net including the TensorFlow package:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "#!pip install pillow\n",
    "from PIL import Image\n",
    "from utils import tile_raster_images\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref2\"></a>\n",
    "<h3>RBM layers</h3>\n",
    "\n",
    "An RBM has two layers. The first layer of the RBM is called the <b>visible</b> (or input layer). Imagine that our toy example, has only vectors with 7 values, so the visible layer must have j=7 input nodes. \n",
    "The second layer is the <b>hidden</b> layer, which possesses i neurons in our case. Each hidden node can have either 0 or 1 values (i.e., si = 1 or si = 0) with a probability that is a logistic function of the inputs it receives from the other j visible units, called for example, p(si = 1). For our toy sample, we'll use 2 nodes in the hidden layer, so i = 2.\n",
    "\n",
    "<center><img src=\"https://ibm.box.com/shared/static/eu26opvcefgls6vnwuo29uwp0nudmokh.png\" alt=\"RBM Model\" style=\"width: 400px;\"></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "     \n",
    "\n",
    "Each node in the first layer also has a <b>bias</b>. We will denote the bias as “v_bias” for the visible units. The <b>v_bias</b> is shared among all visible units.\n",
    "\n",
    "Here we define the <b>bias</b> of second layer as well. We will denote the bias as “h_bias” for the hidden units. The <b>h_bias</b> is shared among all hidden units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "v_bias = tf.placeholder(\"float\", [7])\n",
    "h_bias = tf.placeholder(\"float\", [2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have to define weights among the input layer and hidden layer nodes. In the weight matrix, the number of rows are equal to the input nodes, and the number of columns are equal to the output nodes. Let <b>W</b> be the Tensor of 7x2 (7 - number of visible neurons, 2 - number of hidden neurons) that represents weights between neurons. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = tf.constant(np.random.normal(loc=0.0, scale=1.0, size=(7, 2)).astype(np.float32))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref3\"></a>\n",
    "<h3>What RBM can do after training?</h3>\n",
    "Think RBM as a model that has been trained based on images of a dataset of many SUV and Sedan cars. Also, imagine that the RBM network has only two hidden nodes, one for the weight and, and one for the size of cars, which in a sense, their different configurations represent different cars, one represent SUV cars and one for Sedan. In a training process, through many forward and backward passes, RBM adjust its weights to send a stronger signal to either the SUV node (0, 1) or the Sedan node (1, 0) in the hidden layer, given the pixels of images. Now, given a SUV in hidden layer, which distribution of pixels should we expect? RBM can give you 2 things. First, it encodes your images in hidden layer. Second, it gives you the probability of observing a case, given some hidden values.\n",
    "\n",
    "\n",
    "<h3>How to inference?</h3>\n",
    "\n",
    "RBM has two phases:\n",
    "<ul>\n",
    "    <li>Forward Pass</li>  \n",
    "    <li>Backward Pass or Reconstruction</li>\n",
    "</ul>\n",
    "\n",
    "<b>Phase 1) Forward pass:</b>  Input one training sample (one image) <b>X</b> through all visible nodes, and pass it to all hidden nodes. Processing happens in each node in the hidden layer. This computation begins by making stochastic decisions about whether to transmit that input or not (i.e. to determine the state of each hidden layer). At the hidden layer's nodes, <b>X</b> is multiplied by a <b>$W_{ij}$</b> and added to <b>h_bias</b>. The result of those two operations is fed into the sigmoid function, which produces the node’s output, $p({h_j})$, where j is the unit number. \n",
    "\n",
    "\n",
    "$p({h_j})= \\sigma(\\sum_i w_{ij} x_i)$, where $\\sigma()$ is the logistic function.\n",
    "\n",
    "\n",
    "Now lets see what $p({h_j})$ represents. In fact, it is the probabilities of the hidden units. And, all values together are called <b>probability distribution</b>. That is, RBM uses inputs x to make predictions about hidden node activations. For example, imagine that the values of $h_p$ for the first training item is [0.51 0.84]. It tells you what is the conditional probability for each hidden neuron to be at Phase 1): \n",
    "<ul>\n",
    "    <li>p($h_{1}$ = 1|V) = 0.51</li>\n",
    "    <li>($h_{2}$ = 1|V) = 0.84</li>  \n",
    "</ul>\n",
    "\n",
    "As a result, for each row in the training set, <b>a vector/tensor</b> is generated, which in our case it is of size [1x2], and totally n vectors ($p({h})$=[nx2]). \n",
    "\n",
    "We then turn unit $h_j$ on with probability $p(h_{j}|V)$, and turn it off with probability $1 - p(h_{j}|V)$.\n",
    "\n",
    "Therefore, the conditional probability of a configuration of h given v (for a training sample) is:\n",
    "\n",
    "$$p(\\mathbf{h} \\mid \\mathbf{v}) = \\prod_{j=0}^H p(h_j \\mid \\mathbf{v})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, sample a hidden activation vector <b>h</b> from this probability distribution $p({h_j})$. That is, we sample the activation vector from the probability distribution of hidden layer values. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we go further, let's look at a toy example for one case out of all input. Assume that we have a trained RBM, and a very simple input vector such as [1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0], lets see what would be the output of forward pass:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input:  [[1. 0. 0. 1. 0. 0. 0.]]\n",
      "hb:  [0.1 0.1]\n",
      "w:  [[ 1.6985698  -0.32507902]\n",
      " [ 1.2987217  -0.05548834]\n",
      " [-0.46908382 -0.65388656]\n",
      " [-0.61916614 -0.1963053 ]\n",
      " [-1.3157144  -1.368783  ]\n",
      " [-1.9358245   1.1250753 ]\n",
      " [ 2.191544    0.11812211]]\n",
      "p(h|v):  [[0.7648406  0.39618555]]\n",
      "Shape h_prob: [1 2]\n",
      "PICK ANY from a uni random where shape is the same as above: [[0.7053883 0.7034348]]\n",
      "difference h_prob - pick: [[0.6278297  0.11343899]]\n",
      "sign(h_prob - pick): [[ 1. -1.]]\n",
      "h0 states: [[1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "sess = tf.Session()\n",
    "X = tf.constant([[1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]])\n",
    "v_state = X\n",
    "print (\"Input: \", sess.run(v_state))\n",
    "\n",
    "h_bias = tf.constant([0.1, 0.1])\n",
    "print (\"hb: \", sess.run(h_bias))\n",
    "print (\"w: \", sess.run(W))\n",
    "\n",
    "# Calculate the probabilities of turning the hidden units on:\n",
    "h_prob = tf.nn.sigmoid(tf.matmul(v_state, W) + h_bias)  #probabilities of the hidden units\n",
    "print (\"p(h|v): \", sess.run(h_prob))\n",
    "\n",
    "# Draw samples from the distribution:\n",
    "#Pvr\n",
    "temp1 = tf.shape(h_prob)\n",
    "temp2 = tf.random_uniform(tf.shape(h_prob))\n",
    "temp3 = h_prob - tf.random_uniform(tf.shape(h_prob))\n",
    "temp4 = tf.sign(h_prob - tf.random_uniform(tf.shape(h_prob)))\n",
    "print (\"Shape h_prob:\", sess.run(temp1))\n",
    "print (\"PICK ANY from a uni random where shape is the same as above:\", sess.run(temp2))\n",
    "print (\"difference h_prob - pick:\", sess.run(temp3))\n",
    "print (\"sign(h_prob - pick):\", sess.run(temp4))\n",
    "#Pvr\n",
    "h_state = tf.nn.relu(tf.sign(h_prob - tf.random_uniform(tf.shape(h_prob)))) #states\n",
    "print (\"h0 states:\", sess.run(h_state))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Phase 2) Backward Pass (Reconstruction):</b>\n",
    "The RBM reconstructs data by making several forward and backward passes between the visible and hidden layers.\n",
    "\n",
    "So, in the second phase (i.e. reconstruction phase), the samples from the hidden layer (i.e. h) play the role of input. That is, <b>h</b> becomes the input in the backward pass. The same weight matrix and visible layer biases are used to go through the sigmoid function. The produced output is a reconstruction which is an approximation of the original input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b:  [0.1 0.2 0.1 0.1 0.1 0.2 0.1]\n",
      "p(vi∣h):  [[0.85797477 0.8173837  0.40876243 0.37304726 0.22869152 0.14984408\n",
      "  0.9081743 ]]\n",
      "v probability states:  [[1. 1. 0. 1. 0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "vb = tf.constant([0.1, 0.2, 0.1, 0.1, 0.1, 0.2, 0.1])\n",
    "print (\"b: \", sess.run(vb))\n",
    "v_prob = sess.run(tf.nn.sigmoid(tf.matmul(h_state, tf.transpose(W)) + vb))\n",
    "print (\"p(vi∣h): \", v_prob)\n",
    "v_state = tf.nn.relu(tf.sign(v_prob - tf.random_uniform(tf.shape(v_prob))))\n",
    "print (\"v probability states: \", sess.run(v_state))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RBM learns a probability distribution over the input, and then, after being trained, the RBM can generate new samples from the learned probability distribution. As you know, <b>probability distribution</b>, is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.\n",
    "\n",
    "The (conditional) probability distribution over the visible units v is given by\n",
    "\n",
    "$p(\\mathbf{v} \\mid \\mathbf{h}) = \\prod_{i=0}^V p(v_i \\mid \\mathbf{h}),$\n",
    "\n",
    "\n",
    "where,\n",
    "\n",
    "$p(v_i \\mid \\mathbf{h}) = \\sigma\\left( a_i + \\sum_{j=0}^H w_{ji} h_j \\right)$\n",
    "\n",
    "so, given current state of hidden units and weights, what is the probability of generating [1. 0. 0. 1. 0. 0. 0.] in reconstruction phase, based on the above <b>probability distribution</b> function?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 1. 0. 0. 0.]]\n",
      "[0.85797477 0.8173837  0.40876243 0.37304726 0.22869152 0.14984408\n",
      " 0.9081743 ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.0020808030394455653"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp = sess.run(X)\n",
    "print(inp)\n",
    "print(v_prob[0])\n",
    "v_probability = 1\n",
    "for elm, p in zip(inp[0],v_prob[0]) :\n",
    "    if elm ==1:\n",
    "        v_probability *= p\n",
    "    else:\n",
    "        v_probability *= (1-p)\n",
    "v_probability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How similar X and V vectors are? Of course, the reconstructed values most likely will not look anything like the input vector because our network has not trained yet. Our objective is to train the model in such a way that the input vector and reconstructed vector to be same. Therefore, based on how different the input values look to the ones that we just reconstructed, the weights are adjusted. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<h2>MNIST</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will be using the MNIST dataset to practice the usage of RBMs. The following cell loads the MNIST dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From <ipython-input-9-a0c1bc5755ed>:1: read_data_sets (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use alternatives such as official/mnist/dataset.py from tensorflow/models.\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:260: maybe_download (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please write your own downloading logic.\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/base.py:252: _internal_retry.<locals>.wrap.<locals>.wrapped_fn (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use urllib or similar directly.\n",
      "Successfully downloaded train-images-idx3-ubyte.gz 9912422 bytes.\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:262: extract_images (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use tf.data to implement this functionality.\n",
      "Extracting MNIST_data/train-images-idx3-ubyte.gz\n",
      "Successfully downloaded train-labels-idx1-ubyte.gz 28881 bytes.\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:267: extract_labels (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use tf.data to implement this functionality.\n",
      "Extracting MNIST_data/train-labels-idx1-ubyte.gz\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:110: dense_to_one_hot (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use tf.one_hot on tensors.\n",
      "Successfully downloaded t10k-images-idx3-ubyte.gz 1648877 bytes.\n",
      "Extracting MNIST_data/t10k-images-idx3-ubyte.gz\n",
      "Successfully downloaded t10k-labels-idx1-ubyte.gz 4542 bytes.\n",
      "Extracting MNIST_data/t10k-labels-idx1-ubyte.gz\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:290: DataSet.__init__ (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use alternatives such as official/mnist/dataset.py from tensorflow/models.\n"
     ]
    }
   ],
   "source": [
    "mnist = input_data.read_data_sets(\"MNIST_data/\", one_hot=True)\n",
    "trX, trY, teX, teY = mnist.train.images, mnist.train.labels, mnist.test.images, mnist.test.labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at the dimension of the images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(784,)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trX[1].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MNIST images have 784 pixels, so the visible layer must have 784 input nodes.  For our case, we'll use 50 nodes in the hidden layer, so i = 50."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vb = tf.placeholder(\"float\", [784])\n",
    "hb = tf.placeholder(\"float\", [50])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let <b>W</b> be the Tensor of 784x50 (784 - number of visible neurons, 50 - number of hidden neurons) that represents weights between the neurons. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "W = tf.placeholder(\"float\", [784, 50])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets define the visible layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "v0_state = tf.placeholder(\"float\", [None, 784])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can define hidden layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "h0_prob = tf.nn.sigmoid(tf.matmul(v0_state, W) + hb)  #probabilities of the hidden units\n",
    "h0_state = tf.nn.relu(tf.sign(h0_prob - tf.random_uniform(tf.shape(h0_prob)))) #sample_h_given_X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we define reconstruction part:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "v1_prob = tf.nn.sigmoid(tf.matmul(h0_state, tf.transpose(W)) + vb) \n",
    "v1_state = tf.nn.relu(tf.sign(v1_prob - tf.random_uniform(tf.shape(v1_prob)))) #sample_v_given_h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is objective function?</h3>\n",
    "\n",
    "<b>Goal</b>: Maximize the likelihood of our data being drawn from that distribution\n",
    "\n",
    "<b>Calculate error:</b>  \n",
    "In each epoch, we compute the \"error\" as a sum of the squared difference between step 1 and step n,\n",
    "e.g the error shows the difference between the data and its reconstruction.\n",
    "\n",
    "<b>Note:</b> tf.reduce_mean computes the mean of elements across dimensions of a tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "err = tf.reduce_mean(tf.square(v0_state - v1_state))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref4\"></a>\n",
    "<h3>How to train the model?</h3>\n",
    "<b>Warning!!</b> The following part discuss how to train the model which needs some algebra background. Still, you can skip this part and run the next cells.\n",
    "\n",
    "As mentioned, we want to give a high probability to the input data we train on. So, in order to train an RBM, we have to maximize the product of probabilities assigned to all rows v (images) in the training set V (a matrix, where each row of it is treated as a visible vector v):\n",
    "\n",
    "<img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/d42e9f5aad5e1a62b11b119c9315236383c1864a\">\n",
    "\n",
    "\n",
    "Which is equivalent, maximizing the expected log probability of V:\n",
    "\n",
    "\n",
    "<img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/ba0ceed99dca5ff1d21e5ace23f5f2223f19efc0\">\n",
    "\n",
    "\n",
    "So, we have to update the weights wij  to increase p(v) for all v in our training data during training. So we have to calculate the derivative:\n",
    "\n",
    "\n",
    "$$\\frac{\\partial \\log p(\\mathbf v)}{\\partial w_{ij}}$$\n",
    "\n",
    "This cannot be easily done by typical <b>gradient descent (SGD)</b>, so we can use another approach, which has 2 steps:\n",
    "<ol>\n",
    "    <li>Gibbs Sampling</li>\n",
    "    <li>Contrastive Divergence</li>\n",
    "</ol>    \n",
    "    \n",
    "<h3>Gibbs Sampling</h3>   \n",
    "First, given an input vector v we are using p(h|v) for prediction of the hidden values h. \n",
    "<ul>\n",
    "    <li>$p(h|v) = sigmoid(X \\otimes W + hb)$</li>\n",
    "    <li>h0 = sampleProb(h0)</li>\n",
    "</ul>\n",
    "    \n",
    "Then, knowing the hidden values, we use p(v|h) for reconstructing of new input values v. \n",
    "<ul>\n",
    "    <li>$p(v|h) = sigmoid(h0 \\otimes transpose(W) + vb)$</li>\n",
    "    <li>$v1 = sampleProb(v1)$  (Sample v given h)</li>\n",
    "</ul>\n",
    "        \n",
    "This process is repeated k times. After k iterations we obtain an other input vector vk which was recreated from original input values v0 or X.\n",
    "\n",
    "Reconstruction steps:\n",
    "<ul>\n",
    "    <li> Get one data point from data set, like <i>x</i>, and pass it through the net</li>\n",
    "    <li>Pass 0: (x)  $\\Rightarrow$ (h0) $\\Rightarrow$  (v1)   (v1 is reconstruction of the first pass)</li>\n",
    "    <li>Pass 1: (v1) $\\Rightarrow$  (h1) $\\Rightarrow$  (v2)   (v2 is reconstruction of the second pass)</li>\n",
    "    <li>Pass 2: (v2) $\\Rightarrow$  (h2) $\\Rightarrow$  (v3)   (v3 is reconstruction of the third pass)</li>\n",
    "    <li>Pass n: (vk) $\\Rightarrow$  (hk+1) $\\Rightarrow$  (vk+1)(vk is reconstruction of the nth pass)</li>\n",
    "</ul>\n",
    "        \n",
    "<h4>What is sampling here (sampleProb)?</h4>\n",
    "\n",
    "In forward pass: We randomly set the values of each hi to be 1 with probability $sigmoid(v \\otimes W + hb)$.  \n",
    "- To sample h given v means to sample from the conditional probability distribution P(h|v). It means that you are asking what are the probabilities of getting a specific set of values for the hidden neurons, given the values v for the visible neurons, and sampling from this probability distribution. \n",
    "In reconstruction: We randomly set the values of each vi to be 1 with probability $ sigmoid(h \\otimes transpose(W) + vb)$.\n",
    "\n",
    "<h3>contrastive divergence (CD-k)</h3>\n",
    "The update of the weight matrix is done during the Contrastive Divergence step. \n",
    "\n",
    "Vectors v0 and vk are used to calculate the activation probabilities for hidden values h0 and hk. The difference between the outer products of those probabilities with input vectors v0 and vk results in the update matrix:\n",
    "\n",
    "\n",
    "$\\Delta W =v0 \\otimes h0 - vk \\otimes hk$ \n",
    "\n",
    "Contrastive Divergence is actually matrix of values that is computed and used to adjust values of the W matrix. Changing W incrementally leads to training of W values. Then on each step (epoch), W is updated to a new value W' through the equation below:\n",
    "\n",
    "$W' = W + alpha * \\Delta W$ \n",
    "\n",
    " \n",
    "<b>What is Alpha?</b>  \n",
    "Here, alpha is some small step rate and is also known as the \"learning rate\".\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, lets assume that k=1, that is we just get one more step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "h1_prob = tf.nn.sigmoid(tf.matmul(v1_state, W) + hb)\n",
    "h1_state = tf.nn.relu(tf.sign(h1_prob - tf.random_uniform(tf.shape(h1_prob)))) #sample_h_given_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.01\n",
    "W_Delta = tf.matmul(tf.transpose(v0_state), h0_prob) - tf.matmul(tf.transpose(v1_state), h1_prob)\n",
    "update_w = W + alpha * W_Delta\n",
    "update_vb = vb + alpha * tf.reduce_mean(v0_state - v1_state, 0)\n",
    "update_hb = hb + alpha * tf.reduce_mean(h0_state - h1_state, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start a session and initialize the variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "cur_w = np.zeros([784, 50], np.float32)\n",
    "cur_vb = np.zeros([784], np.float32)\n",
    "cur_hb = np.zeros([50], np.float32)\n",
    "prv_w = np.zeros([784, 50], np.float32)\n",
    "prv_vb = np.zeros([784], np.float32)\n",
    "prv_hb = np.zeros([50], np.float32)\n",
    "sess = tf.Session()\n",
    "init = tf.global_variables_initializer()\n",
    "sess.run(init)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at the error of the first run:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48157495"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sess.run(err, feed_dict={v0_state: trX, W: prv_w, vb: prv_vb, hb: prv_hb})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0 reconstruction error: 0.085421\n",
      "Epoch: 1 reconstruction error: 0.081911\n",
      "Epoch: 2 reconstruction error: 0.082109\n",
      "Epoch: 3 reconstruction error: 0.081973\n",
      "Epoch: 4 reconstruction error: 0.081486\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Parameters\n",
    "epochs = 5\n",
    "batchsize = 100\n",
    "weights = []\n",
    "errors = []\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    for start, end in zip( range(0, len(trX), batchsize), range(batchsize, len(trX), batchsize)):\n",
    "        batch = trX[start:end]\n",
    "        cur_w = sess.run(update_w, feed_dict={ v0_state: batch, W: prv_w, vb: prv_vb, hb: prv_hb})\n",
    "        cur_vb = sess.run(update_vb, feed_dict={v0_state: batch, W: prv_w, vb: prv_vb, hb: prv_hb})\n",
    "        cur_hb = sess.run(update_hb, feed_dict={ v0_state: batch, W: prv_w, vb: prv_vb, hb: prv_hb})\n",
    "        prv_w = cur_w\n",
    "        prv_vb = cur_vb\n",
    "        prv_hb = cur_hb\n",
    "        if start % 10000 == 0:\n",
    "            errors.append(sess.run(err, feed_dict={v0_state: trX, W: cur_w, vb: cur_vb, hb: cur_hb}))\n",
    "            weights.append(cur_w)\n",
    "    print ('Epoch: %d' % epoch,'reconstruction error: %f' % errors[-1])\n",
    "plt.plot(errors)\n",
    "plt.xlabel(\"Batch Number\")\n",
    "plt.ylabel(\"Error\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the final weight after training?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.77074194 -0.7960384  -0.76348436 ... -0.8766602  -0.7692333\n",
      "  -0.81857705]\n",
      " [-0.28871512 -0.26057094 -0.3087913  ... -0.27256432 -0.27865294\n",
      "  -0.27733067]\n",
      " [-0.49493924 -0.5899048  -0.60941553 ... -0.5515836  -0.57255983\n",
      "  -0.55811256]\n",
      " ...\n",
      " [-0.21773648 -0.25956392 -0.2739336  ... -0.2328246  -0.25592464\n",
      "  -0.19228715]\n",
      " [-0.43991736 -0.39075482 -0.41898558 ... -0.39897156 -0.38733056\n",
      "  -0.41930798]\n",
      " [-1.4734432  -1.3603743  -1.3141837  ... -1.3366165  -1.4259807\n",
      "  -1.3282248 ]]\n"
     ]
    }
   ],
   "source": [
    "uw = weights[-1].T\n",
    "print (uw) # a weight matrix of shape (50,784)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref5\"></a>\n",
    "<h3>Learned features</h3> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can take each hidden unit and visualize the connections between that hidden unit and each element in the input vector. In our case, we have 50 hidden units. Lets visualize those."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the current weights:\n",
    "<b>tile_raster_images</b> helps in generating an easy to grasp image from a set of samples or weights. It transform the <b>uw</b> (with one flattened image per row of size 784), into an array (of size $25\\times20$) in which images are reshaped and laid out like tiles on a floor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tile_raster_images(X=cur_w.T, img_shape=(28, 28), tile_shape=(5, 10), tile_spacing=(1, 1))\n",
    "import matplotlib.pyplot as plt\n",
    "from PIL import Image\n",
    "%matplotlib inline\n",
    "image = Image.fromarray(tile_raster_images(X=cur_w.T, img_shape=(28, 28) ,tile_shape=(5, 10), tile_spacing=(1, 1)))\n",
    "### Plot image\n",
    "plt.rcParams['figure.figsize'] = (18.0, 18.0)\n",
    "imgplot = plt.imshow(image)\n",
    "imgplot.set_cmap('gray')  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each tile in the above visualization corresponds to a vector of connections between a hidden unit and visible layer's units. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at one of the learned weights corresponding to one of hidden units for example. In this particular square, the gray color represents weight = 0, and the whiter it is, the more positive the weights are (closer to 1). Conversely, the darker pixels are, the more negative the weights. The positive pixels will increase the probability of activation in hidden units (after multiplying by input/visible pixels), and negative pixels will decrease the probability of a unit hidden to be 1 (activated). So, why is this important?  So we can see that this specific square (hidden unit) can detect a feature (e.g. a \"/\" shape) and if it exists in the input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from PIL import Image\n",
    "image = Image.fromarray(tile_raster_images(X =cur_w.T[10:11], img_shape=(28, 28),tile_shape=(1, 1), tile_spacing=(1, 1)))\n",
    "### Plot image\n",
    "plt.rcParams['figure.figsize'] = (4.0, 4.0)\n",
    "imgplot = plt.imshow(image)\n",
    "imgplot.set_cmap('gray')  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the reconstruction of an image now. Imagine that we have a destructed image of figure 3. Lets see if our trained network can fix it:\n",
    "\n",
    "First we plot the image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2018-11-05 09:33:33--  https://ibm.box.com/shared/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg\n",
      "Resolving ibm.box.com (ibm.box.com)... 107.152.27.197\n",
      "Connecting to ibm.box.com (ibm.box.com)|107.152.27.197|:443... connected.\n",
      "HTTP request sent, awaiting response... 301 Moved Permanently\n",
      "Location: https://ibm.ent.box.com/shared/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg [following]\n",
      "--2018-11-05 09:33:33--  https://ibm.ent.box.com/shared/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg\n",
      "Resolving ibm.ent.box.com (ibm.ent.box.com)... 107.152.26.211, 107.152.27.211\n",
      "Connecting to ibm.ent.box.com (ibm.ent.box.com)|107.152.26.211|:443... connected.\n",
      "HTTP request sent, awaiting response... 302 Found\n",
      "Location: https://public.boxcloud.com/d/1/b1!Ki6cSSdjGda9GSLdnKcDLFU8M7qyLu11J2TaGCcyD-lxBYOVhuhUIYe3P3j0dVJx4vwHIJT1aH_1ZHDXpu0EOtmmdpBfxr2pZj-GFFavxm_W0D6CxJT_bvOhy5VGt0vlEmcvJWW7vNBASL0EwSIDd7MAdu0KaMl7MUrwJ0jO-GFT63X-DXq9XxxLzRpBtD5nGfzWs50NiOYEwKxHuo-vuE5tEroA8Hl6QYY8YPNLQ87xoWxEpYFBGdcCjSV3WoziimVCMdULBQCx1ROt81-ZgLKvEMvXNzHvXnmbpxaI4Wssja5WdN9DkvJKwQKXKTszbLI8md-bfm4ouybijkq4O3pTDNrxpCjs7rFmF0OFey-rn0vOXydSVqosjHS2hb9QQP_d1PP858y743-a6epWBtyXToXHoXaM_0GVHnEyVIof48vZfOWWF1R1sdYNLGwtBztn18GGXitaaYpsfGd8vRudBUVy65wnTELHC8i2aUEjuS-1d9yzXrVKzv3XQjE5vFhYT6W8nzclGozNN-9mrRjDmTxZKKt8_Eja7Tfn7l_NXaraAuf8eDASmjE9b1g1Ti0S1UN0gn1iraqxyD-ano0bzdbPwh6M6SPNIFHis9BqhSRtXzYGLBEBAbXeGwmerUivwYrUHefT-TF8740h6hOS3N67DNyTdCQO-t5ucEWyJHaXjv2B3Z7wBGjZECt8qwbILH_d88OysjIB35wIjDN-z6uofMDibkQ3HV-nd5zlK4FX2YjxePsFM_N2PDALegjoASjRDWna2-KoZmlKQgGEX9bfwcy7kz5aAvlqFlkyC0yLiBYB7k8iXpHTyx5Xv5AobYFgEPHvxYgR1VH7ESrogX5C-shRj4Q1j6YOlq_UbjDM_84MvKMuMT7FJzcoq7ThXCrTDBHBnNTOH2yioo_ydu8hF2WvgiVFiT8o4K6OqsK9hHwTucY1ICSs5TVQnNywwS5S_lWXqCczkRvuovyN6d-4GZwMYEjc836RLKEAyV1NDhre4Gh7QtfnuxyiPEZTYqnrYrSRGas6YjcO4NhQEYj2h5tZcK1XX5x4vBnG1XnWKufsXjhkdzNRDT5q9NN3xamw6gyCyiXKPIp0HpTqfqoZ-V7NYaVmItl8s5yB9iYFa9nD2w0z0h6QZgIca0DK1rxaO2aY8PsmPm3NhQ983tf6ZIkFyQK9NmobAclHTiZXYRRlHNm0XBhyyh78XfCvyI92akou8xCf1eWpFDCCXiB9ho9LtC8ERBqJXy6_jXQggLuEIxOIja9x0Kb7WLv3awvDfNpENvWKV1H0W5B7sB_pc1VfmvLaXDlKabql40fwjaU1M_Yh/download [following]\n",
      "--2018-11-05 09:33:34--  https://public.boxcloud.com/d/1/b1!Ki6cSSdjGda9GSLdnKcDLFU8M7qyLu11J2TaGCcyD-lxBYOVhuhUIYe3P3j0dVJx4vwHIJT1aH_1ZHDXpu0EOtmmdpBfxr2pZj-GFFavxm_W0D6CxJT_bvOhy5VGt0vlEmcvJWW7vNBASL0EwSIDd7MAdu0KaMl7MUrwJ0jO-GFT63X-DXq9XxxLzRpBtD5nGfzWs50NiOYEwKxHuo-vuE5tEroA8Hl6QYY8YPNLQ87xoWxEpYFBGdcCjSV3WoziimVCMdULBQCx1ROt81-ZgLKvEMvXNzHvXnmbpxaI4Wssja5WdN9DkvJKwQKXKTszbLI8md-bfm4ouybijkq4O3pTDNrxpCjs7rFmF0OFey-rn0vOXydSVqosjHS2hb9QQP_d1PP858y743-a6epWBtyXToXHoXaM_0GVHnEyVIof48vZfOWWF1R1sdYNLGwtBztn18GGXitaaYpsfGd8vRudBUVy65wnTELHC8i2aUEjuS-1d9yzXrVKzv3XQjE5vFhYT6W8nzclGozNN-9mrRjDmTxZKKt8_Eja7Tfn7l_NXaraAuf8eDASmjE9b1g1Ti0S1UN0gn1iraqxyD-ano0bzdbPwh6M6SPNIFHis9BqhSRtXzYGLBEBAbXeGwmerUivwYrUHefT-TF8740h6hOS3N67DNyTdCQO-t5ucEWyJHaXjv2B3Z7wBGjZECt8qwbILH_d88OysjIB35wIjDN-z6uofMDibkQ3HV-nd5zlK4FX2YjxePsFM_N2PDALegjoASjRDWna2-KoZmlKQgGEX9bfwcy7kz5aAvlqFlkyC0yLiBYB7k8iXpHTyx5Xv5AobYFgEPHvxYgR1VH7ESrogX5C-shRj4Q1j6YOlq_UbjDM_84MvKMuMT7FJzcoq7ThXCrTDBHBnNTOH2yioo_ydu8hF2WvgiVFiT8o4K6OqsK9hHwTucY1ICSs5TVQnNywwS5S_lWXqCczkRvuovyN6d-4GZwMYEjc836RLKEAyV1NDhre4Gh7QtfnuxyiPEZTYqnrYrSRGas6YjcO4NhQEYj2h5tZcK1XX5x4vBnG1XnWKufsXjhkdzNRDT5q9NN3xamw6gyCyiXKPIp0HpTqfqoZ-V7NYaVmItl8s5yB9iYFa9nD2w0z0h6QZgIca0DK1rxaO2aY8PsmPm3NhQ983tf6ZIkFyQK9NmobAclHTiZXYRRlHNm0XBhyyh78XfCvyI92akou8xCf1eWpFDCCXiB9ho9LtC8ERBqJXy6_jXQggLuEIxOIja9x0Kb7WLv3awvDfNpENvWKV1H0W5B7sB_pc1VfmvLaXDlKabql40fwjaU1M_Yh/download\n",
      "Resolving public.boxcloud.com (public.boxcloud.com)... 107.152.26.200\n",
      "Connecting to public.boxcloud.com (public.boxcloud.com)|107.152.26.200|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 24383 (24K) [image/jpeg]\n",
      "Saving to: ‘destructed3.jpg’\n",
      "\n",
      "destructed3.jpg     100%[=====================>]  23.81K  --.-KB/s   in 0.02s  \n",
      "\n",
      "2018-11-05 09:33:34 (1016 KB/s) - ‘destructed3.jpg’ saved [24383/24383]\n",
      "\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=181x181 at 0x7F1994E4B7F0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "!wget -O destructed3.jpg  https://ibm.box.com/shared/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg\n",
    "img = Image.open('destructed3.jpg')\n",
    "img"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's pass this image through the net:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert the image to a 1d numpy array\n",
    "sample_case = np.array(img.convert('I').resize((28,28))).ravel().reshape((1, -1))/255.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Feed the sample case into the network and reconstruct the output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability nodes in hidden layer: [[0.00000000e+00 1.55519963e-24 3.53393960e-04 6.90521693e-16\n",
      "  3.80868209e-03 2.82181842e-20 2.58419372e-22 9.99999762e-01\n",
      "  1.23643658e-17 1.10987946e-03 2.50576576e-30 9.99943972e-01\n",
      "  1.12329555e-10 3.56651921e-32 4.00661934e-21 2.31762889e-17\n",
      "  2.19517446e-07 2.76006622e-23 3.29447794e-33 2.89662457e-05\n",
      "  1.18967432e-22 3.90922528e-21 2.14417670e-02 1.07781500e-01\n",
      "  2.80150625e-11 4.61764174e-08 0.00000000e+00 2.41053321e-16\n",
      "  6.98573919e-22 4.79164326e-19 1.00000000e+00 4.60467078e-26\n",
      "  7.62108069e-15 7.39542773e-23 9.19355009e-11 5.97559439e-04\n",
      "  4.56990229e-25 9.32167709e-01 3.49569968e-15 1.00000000e+00\n",
      "  2.49714779e-31 2.13731731e-16 1.18906967e-24 9.98603523e-01\n",
      "  1.60818060e-11 2.79210911e-17 7.87111208e-20 8.75939958e-16\n",
      "  4.15141812e-06 1.00000000e+00]]\n",
      "activated nodes in hidden layer: [[0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      "  0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 1. 0. 0. 0. 0.\n",
      "  0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "hh0_p = tf.nn.sigmoid(tf.matmul(v0_state, W) + hb)\n",
    "#hh0_s = tf.nn.relu(tf.sign(hh0_p - tf.random_uniform(tf.shape(hh0_p)))) \n",
    "hh0_s = tf.round(hh0_p)\n",
    "hh0_p_val,hh0_s_val  = sess.run((hh0_p, hh0_s), feed_dict={ v0_state: sample_case, W: prv_w, hb: prv_hb})\n",
    "print(\"Probability nodes in hidden layer:\" ,hh0_p_val)\n",
    "print(\"activated nodes in hidden layer:\" ,hh0_s_val)\n",
    "\n",
    "# reconstruct\n",
    "vv1_p = tf.nn.sigmoid(tf.matmul(hh0_s_val, tf.transpose(W)) + vb)\n",
    "rec_prob = sess.run(vv1_p, feed_dict={ hh0_s: hh0_s_val, W: prv_w, vb: prv_vb})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we plot the reconstructed image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = Image.fromarray(tile_raster_images(X=rec_prob, img_shape=(28, 28),tile_shape=(1, 1), tile_spacing=(1, 1)))\n",
    "plt.rcParams['figure.figsize'] = (4.0, 4.0)\n",
    "imgplot = plt.imshow(img)\n",
    "imgplot.set_cmap('gray') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "## Want to learn more?\n",
    "\n",
    "Running deep learning programs usually needs a high performance platform. __PowerAI__ speeds up deep learning and AI. Built on IBM’s Power Systems, __PowerAI__ is a scalable software platform that accelerates deep learning and AI with blazing performance for individual users or enterprises. The __PowerAI__ platform supports popular machine learning libraries and dependencies including TensorFlow, Caffe, Torch, and Theano. You can use [PowerAI on IMB Cloud](https://cocl.us/ML0120EN_PAI).\n",
    "\n",
    "Also, you can use __Watson Studio__ to run these notebooks faster with bigger datasets.__Watson Studio__ is IBM’s leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, __Watson Studio__ enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of __Watson Studio__ users today with a free account at [Watson Studio](https://cocl.us/ML0120EN_DSX).This is the end of this lesson. Thank you for reading this notebook, and good luck on your studies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thanks for completing this lesson!\n",
    "\n",
    "Notebook created by: <a href = \"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References:\n",
    "https://en.wikipedia.org/wiki/Restricted_Boltzmann_machine  \n",
    "http://deeplearning.net/tutorial/rbm.html  \n",
    "http://www.cs.utoronto.ca/~hinton/absps/netflixICML.pdf<br>\n",
    "http://imonad.com/rbm/restricted-boltzmann-machine/  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "Copyright &copy; 2018 [Cognitive Class](https://cocl.us/DX0108EN_CC). This notebook and its source code are released under the terms of the [MIT License](https://bigdatauniversity.com/mit-license/)."
   ]
  }
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