Restricted Boltzmann Machine.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",
    "<b><center>RESTRICTED BOLTZMANN MACHINES</center></b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Introduction</h2>\n",
    "\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",
    "<b>Why are RBMs important?</b>\n",
    "It can automatically extract <b>meaningful</b> features from a given input.\n",
    "\n",
    "\n",
    "<b>How does it work?</b>\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",
    "<b>What are the applications of RBM?</b>\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",
    "<b>Is RBM a generative or Discriminative model?</b>\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. \n",
    "\n",
    "<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",
    "<hr>\n",
    "\n",
    "<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>\n",
    "<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: 600px;height: 250px\"></center>\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>\n",
    "<a id=\"ref3\"></a>\n",
    "<h3>What RBM can do after training?</h3><br>\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 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",
    "$$p(\\mathbf{h} \\mid \\mathbf{v}) = \\prod_{j=0}^H p(h_j \\mid \\mathbf{v})$$\n",
    "\n",
    "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. \n",
    "\n",
    "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": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input:  [[1. 0. 0. 1. 0. 0. 0.]]\n",
      "hb:  [0.1 0.1]\n",
      "w:  [[ 0.8217398   0.34932598]\n",
      " [ 2.6944723  -1.7148539 ]\n",
      " [-0.9212223  -0.9858636 ]\n",
      " [-0.4983426  -0.3947413 ]\n",
      " [ 0.5440313  -0.4099035 ]\n",
      " [ 1.006395   -1.2405086 ]\n",
      " [-0.9080069  -1.1835909 ]]\n",
      "p(h|v):  [[0.60429585 0.5136428 ]]\n",
      "h0 state:  [[0. 0.]]\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",
    "h_state = tf.nn.relu(tf.sign(h_prob - tf.random_uniform(tf.shape(h_prob)))) # states\n",
    "print(\"h0 state: \", 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": 6,
   "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):  [[0.78092515 0.7648792  0.14099069 0.31150687 0.55826604 0.49147245\n",
      "  0.12008792]]\n",
      "v probability states:  [[1. 1. 0. 0. 0. 0. 0.]]\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": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 1. 0. 0. 0.]]\n",
      "[0.78092515 0.7648792  0.14099069 0.31150687 0.55826604 0.49147245\n",
      " 0.12008792]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.009711369046773432"
      ]
     },
     "execution_count": 7,
     "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. \n",
    "<hr>\n",
    "\n",
    "<h2>MNIST</h2><br>\n",
    "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": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From <ipython-input-8-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 D:\\Anaconda3\\envs\\py35\\lib\\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 D:\\Anaconda3\\envs\\py35\\lib\\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",
      "WARNING:tensorflow:From D:\\Anaconda3\\envs\\py35\\lib\\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 D:\\Anaconda3\\envs\\py35\\lib\\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",
      "Extracting MNIST_data/t10k-images-idx3-ubyte.gz\n",
      "Extracting MNIST_data/t10k-labels-idx1-ubyte.gz\n",
      "WARNING:tensorflow:From D:\\Anaconda3\\envs\\py35\\lib\\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": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(784,)"
      ]
     },
     "execution_count": 9,
     "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": 10,
   "metadata": {},
   "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": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = tf.placeholder(\"float\", [784, 50])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets define the visible layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": 13,
   "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": 14,
   "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": 15,
   "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><br>\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><br>  \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)$.\n",
    "\n",
    "<h3>contrastive divergence (CD-k)</h3><br>\n",
    "The update of the weight matrix is done during the Contrastive Divergence step. \n",
    "\n",
    "Vectors v0 and vk are used to calculate the activation probabilities for hidden values h0 and hk. The difference between the outer products of those probabilities with input vectors v0 and vk results in the update matrix:\n",
    "\n",
    "\n",
    "$\\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",
    "Ok, lets assume that k=1, that is we just get one more step:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": 17,
   "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": 18,
   "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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48142385"
      ]
     },
     "execution_count": 19,
     "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": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0 reconstruction error: 0.086482\n",
      "Epoch: 1 reconstruction error: 0.079808\n",
      "Epoch: 2 reconstruction error: 0.079567\n",
      "Epoch: 3 reconstruction error: 0.079671\n",
      "Epoch: 4 reconstruction error: 0.079518\n"
     ]
    }
   ],
   "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])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the final weight after training?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-2.0012238  -1.890688   -1.8718197  ... -1.8873795  -1.925546\n",
      "  -1.9028317 ]\n",
      " [-0.5595136  -0.52825445 -0.46772575 ... -0.54781544 -0.4933334\n",
      "  -0.61015743]\n",
      " [-0.25418773 -0.27484965 -0.28205618 ... -0.30762148 -0.2891643\n",
      "  -0.29715836]\n",
      " ...\n",
      " [-0.41398907 -0.41964677 -0.42335185 ... -0.44537836 -0.39594546\n",
      "  -0.466305  ]\n",
      " [-2.1530535  -2.2775092  -2.2086456  ... -2.2099142  -2.1478693\n",
      "  -2.1990592 ]\n",
      " [-0.79689276 -0.75872576 -0.79046744 ... -0.76899344 -0.83002365\n",
      "  -0.80637515]]\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> \n",
    "\n",
    "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.\n",
    "\n",
    "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": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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. \n",
    "\n",
    "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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=181x181 at 0x2B3C82B7C88>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "!wget --quiet https://ibm.box.com/shared/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg --output-document destructed3.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": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability nodes in hidden layer:  [[3.1524766e-10 1.6430400e-14 7.7055908e-23 7.9692910e-12 2.4095939e-02\n",
      "  2.4901933e-24 1.5482716e-02 1.4891146e-08 2.6737932e-14 1.1412700e-14\n",
      "  4.1993057e-34 9.0944056e-25 8.6681904e-23 4.5823395e-14 7.4268401e-01\n",
      "  1.4814909e-27 3.2071816e-25 6.5558607e-23 1.0000000e+00 9.4976878e-07\n",
      "  1.4619836e-01 4.7917746e-02 9.9999154e-01 5.8232566e-38 3.3554933e-21\n",
      "  3.2747992e-11 0.0000000e+00 9.9977428e-01 9.9413693e-01 0.0000000e+00\n",
      "  5.0773394e-13 1.0310131e-05 1.0000000e+00 4.9792680e-28 1.0000000e+00\n",
      "  4.0188772e-07 3.9474812e-22 8.9628375e-01 1.1643854e-18 2.6977803e-27\n",
      "  2.0087035e-10 5.6313348e-25 5.8783096e-01 1.9965595e-11 1.6201553e-13\n",
      "  2.6987077e-06 1.4529659e-09 1.9712056e-24 3.3836872e-14 2.0791968e-33]]\n",
      "activated nodes in hidden layer:  [[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 1. 0. 0. 0. 1. 0.\n",
      "  0. 0. 0. 1. 1. 0. 0. 0. 1. 0. 1. 0. 0. 1. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.\n",
      "  0. 0.]]\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": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Z/ZeZfWBm75nZPxa3V/raJfpVyevW8rf9ZtYh6UNJiyT1SXpD0h3u/n5LO1LCzHolzXf3yseEzewGSQckPXpyNyQz+1dJe9z9oeIP5yR3/+c26dsDOsWdm5vUt7Kdpf9eFb52jdzxuhGqOPIvlLTJ3Te7+1FJv5J0WwX9aHvuvlbSni/cfJuklcXllRr85Wm5kr61BXfvd/c3i8v7JZ3cWbrS1y7Rr0pUEf6LJG0bcr1P7bXlt0taY2brzWxZ1Z0ZxgUnd0Yqfk6tuD9flN25uZW+sLN027x2tex43WhVhH+43UTaacjhOnf/K0l/I+l7xdtbjMxPJV2qwW3c+iX9qMrOFDtLPynp++6+r8q+DDVMvyp53aoIf5+k7iHXvyJpewX9GJa7by9+7pL0tAY/prSTnSc3SS1+7qq4P//P3Xe6+3F3PyHpZ6rwtSt2ln5S0i/c/ani5spfu+H6VdXrVkX435A0x8xmmdk5kr4taXUF/fgSMxtXfBEjMxsn6etqv92HV0taWlxeKunZCvvyZ9pl5+aynaVV8WvXbjteV3KSTzGU8R+SOiStcPcftrwTwzCzSzR4tJcGZzz+ssq+mdkqST0anPW1U9IPJD0j6XFJF0vaKulb7t7yL95K+tajU9y5uUl9K9tZ+jVV+No1csfrhvSHM/yAmDjDDwiK8ANBEX4gKMIPBEX4gaAIPxAU4QeCIvxAUP8HDQgpJOtk5IoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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.\n",
    "\n",
    "### Thanks for completing this lesson!\n",
    "\n",
    "Notebook created by: <a href = \"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>\n",
    "\n",
    "### 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",
    "\n",
    "<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/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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