03_RBMs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9c1ad2ae",
   "metadata": {},
   "source": [
    "# Restricted Boltzmann Machines\n",
    "\n",
    "For a detailed presentation, refer to the section '**1.4 Boltzmann Machines**' in the file *MachineLearningOverview.pdf*, which is included in the same repository as this notebook.\n",
    "\n",
    "A restricted Boltzmann machine (RBM) is a generative stochastic artificial neural network that can be used for unsupervised learning tasks, such as dimensionality reduction, feature learning, collaborative filtering and topic modeling. RBMs are particularly useful for modeling complex distributions of high-dimensional data, such as images, speech signals, and genomic data and have been successfully applied in a wide range of fields, including computer vision, speech recognition, natural language processing and bioinformatics. RBMs are also used as building blocks for more complex deep learning models, such as deep belief networks and deep autoencoders, which are used for tasks like image and text generation and anomaly detection. They can extract features of some dataset and the output can be used in a supervised model like linear regression or support vector machines for classification."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd9c3c4c",
   "metadata": {},
   "source": [
    "A RBM with 3 visible units and 7 hidden units is presented below:\n",
    "\n",
    "<img src=\"./images/rbm.drawio.png\" width=\"60%\" align=\"center\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a88f847",
   "metadata": {},
   "source": [
    "We will use the *Fashion-MNIST dataset* in order to train a RBM to generate synthetic data that resembles the samples of this dataset. The Fashion-MNIST dataset is a benchmark dataset commonly used in the field of computer vision for image classification tasks. It was created as a more challenging alternative to the popular MNIST dataset, which consists of grayscale images of handwritten digits. It consists of 70,000 grayscale images of size 28x28 pixels, which are divided into 60,000 training images and 10,000 testing images. Each image in the dataset belongs to one of 10 different classes representing different types of clothing and accessories, including T-shirts/tops, trousers, pullovers, dresses, coats, sandals, shirts, sneakers, bags and ankle boots."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af136706",
   "metadata": {},
   "source": [
    "The code is implemented as per *Geoffrey's Hinton* practical guide to training RBMs, *A Practical Guide to Training Restricted Boltzmann Machines Version 1*, *Department of Computer Science, University of Toronto*, August 2, 2010, UTML TR 2010–003: https://www.cs.toronto.edu/~hinton/absps/guideTR.pdf\n",
    "\n",
    "This is a practical guide for tuning RBMs and we just use some of the advice given. Training a RBM is a complex procedure and one should experiment with many variations and heuristics in order to achieve the desired result."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9686f798",
   "metadata": {},
   "source": [
    "First, let us import the necessary packages and load the Fashion-MNIST dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0cd09e47",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training data shape: (60000, 28, 28) (60000,)\n",
      "Testing data shape: (10000, 28, 28) (10000,)\n"
     ]
    }
   ],
   "source": [
    "# hide tensorflow warnings on GPU execution (we will use CPU)\n",
    "from silence_tensorflow import silence_tensorflow\n",
    "silence_tensorflow()\n",
    "\n",
    "from tensorflow import keras\n",
    "from keras.datasets import fashion_mnist\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import time\n",
    "\n",
    "# Load the Fashion-MNIST dataset\n",
    "(x_train, y_train), (x_test, y_test) = fashion_mnist.load_data()\n",
    "\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "\n",
    "# Print the shape of the training data\n",
    "print('Training data shape:', x_train.shape, y_train.shape)\n",
    "\n",
    "# Print the shape of the testing data\n",
    "print('Testing data shape:', x_test.shape, y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62531fec",
   "metadata": {},
   "source": [
    "Let us display some random samples from the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "50ca8399",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the class labels\n",
    "class_labels = ['T-shirt/top', 'Trouser', 'Pullover', 'Dress', 'Coat',\n",
    "                'Sandal', 'Shirt', 'Sneaker', 'Bag', 'Ankle boot']\n",
    "\n",
    "# Generate a random sample of images to display\n",
    "num_images = 5\n",
    "rand_idx = np.random.randint(x_train.shape[0], size=num_images)\n",
    "\n",
    "# Display the images and their labels\n",
    "fig, axes = plt.subplots(1, num_images, figsize=(10,10))\n",
    "for i, ax in enumerate(axes):\n",
    "    ax.imshow(x_train[rand_idx[i]], cmap='gray')\n",
    "    ax.set_title(class_labels[y_train[rand_idx[i]]])\n",
    "    ax.axis('off')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bda7fc0",
   "metadata": {},
   "source": [
    "Then, we reshape the data into arrays and move to normalization (pre-processing) and definition of the RBM hyperparameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3a1dfc0c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reshaped training data shape: (60000, 784)\n",
      "Reshaped testing data shape: (10000, 784)\n"
     ]
    }
   ],
   "source": [
    "training_data = np.reshape(x_train, (x_train.shape[0], x_train.shape[1]*x_train.shape[2]))\n",
    "test_data = np.reshape(x_test, (x_test.shape[0], x_test.shape[1]*x_test.shape[2]))\n",
    "\n",
    "# Print the shape of the reshaped training data\n",
    "print('Reshaped training data shape:', training_data.shape)\n",
    "\n",
    "# Print the shape of the reshaped testing data\n",
    "print('Reshaped testing data shape:', test_data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cfbb5fd6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# normalize\n",
    "threshold = 128\n",
    "training_data = (training_data > np.ones(training_data.shape)*threshold)*1\n",
    "test_data = (test_data > np.ones(test_data.shape)*threshold)*1\n",
    "\n",
    "# define model hyperparameters\n",
    "num_visible = training_data.shape[1]  # number of visible units corresponds to number of features\n",
    "num_hidden = 100  # number of hidden units is set to 100 (sufficient)\n",
    "\n",
    "# define training parameters\n",
    "epochs = 20\n",
    "# for datasets containing small number of equiprobable classes, \n",
    "# the ideal mini-batch size for contrastive divergence equals to the number of classes\n",
    "batch_size = 10\n",
    "# learning rate\n",
    "eta = 0.0125\n",
    "\n",
    "# store reconstruction error for different hyperparameters (for monitoring purposes)\n",
    "rec_err = np.zeros(epochs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d9baadc",
   "metadata": {},
   "source": [
    "Now, we define the RBM class that implements the model that we will train:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7c3b832b",
   "metadata": {},
   "outputs": [],
   "source": [
    "class RBM(object):\n",
    "    # class constructor\n",
    "    def __init__(self, num_visible, num_hidden):\n",
    "        self.num_visible = num_visible\n",
    "        self.num_hidden = num_hidden\n",
    "        \n",
    "        # initialize randomly the biases with a Gaussian of mean 0 and standard deviation 1\n",
    "        self.visible_bias = np.random.normal(loc=0, scale=1, size=(1, num_visible))\n",
    "        self.hidden_bias = np.random.normal(loc=0, scale=1, size=(1, num_hidden))\n",
    "        \n",
    "        # initialize the weight matrix with a Gaussian of mean 0 and standard deviation 0.01\n",
    "        self.weights = np.random.normal(loc=0, scale=0.01, size=(num_visible, num_hidden))\n",
    "        \n",
    "        # the following parameters are used to implement momentum in training as Hinton suggests\n",
    "        self.w_inc = np.zeros(self.weights.shape)\n",
    "        self.a_inc = np.zeros(self.visible_bias.shape)\n",
    "        self.b_inc = np.zeros(self.hidden_bias.shape)\n",
    "        \n",
    "    # Positive phase of contrastive divergence (CD) -- data driven phase\n",
    "    # Sample the states of hidden units based on p_hidden_given_visible\n",
    "    def sample_hidden_given_visible(self, visible_data):\n",
    "        z_hidden = np.dot(visible_data, self.weights) + self.hidden_bias\n",
    "        p_hidden_given_visible = self.sigmoid(z_hidden)\n",
    "        hidden_sample = p_hidden_given_visible > np.random.rand(visible_data.shape[0], self.num_hidden)\n",
    "        # return the probabilities as well, needed for the positive phase of the gradients (data phase)\n",
    "        # less sampling noise --> faster learning\n",
    "        # sampled hidden states are also needed to reconstruct the visible states in the negative phase of CD\n",
    "        return p_hidden_given_visible, hidden_sample\n",
    "    \n",
    "    # Negative phase of CD -- reconstruction driven phase\n",
    "    # Here, do not sample the visible units but use the probabilities instead to avoid sampling noise\n",
    "    def sample_visible_given_hidden(self, hidden_sample):\n",
    "        z_visible = np.dot(hidden_sample, self.weights.T) + self.visible_bias\n",
    "        p_visible_given_hidden = self.sigmoid(z_visible)\n",
    "        return p_visible_given_hidden\n",
    "    \n",
    "    # Sample the hidden states given the visible states (data), then\n",
    "    # get the visible states (reconstructed from hidden samples) as probabilities without sampling\n",
    "    # and at the last update get the hidden states (reconstructed from visible) as probabilities without sampling\n",
    "    def gibbs_sampling(self, visible):\n",
    "        hidden_prob, hidden_sample = self.sample_hidden_given_visible(visible)\n",
    "        visible_recon = self.sample_visible_given_hidden(hidden_sample)\n",
    "        z_hidden_recon_last = np.dot(visible_recon, self.weights) + self.hidden_bias\n",
    "        hidden_recon_last = self.sigmoid(z_hidden_recon_last)\n",
    "        # return reconstructed visible states (probabilities), needed for the negative phase of the gradients\n",
    "        # return hidden probabilities, needed for the positive phase of the gradients\n",
    "        # return last update of hidden units, needed for the negative phase of the gradients\n",
    "        return visible_recon, hidden_prob, hidden_recon_last\n",
    "    \n",
    "    # training the RBM with mini-batches\n",
    "    def train_RBM(self, training_data, epochs, batch_size, eta):\n",
    "        # the goal of the model is to generate synthetic data\n",
    "        # the model is trained using the Contrastive Divergence (CD) algorithm as per Hinton\n",
    "        for epoch in range(epochs):\n",
    "            # partition the dataset in mini-batches, each of size [batch_size]\n",
    "            data_size = len(training_data)\n",
    "            mini_batches = [training_data[i:i+batch_size] for i in range(0, data_size, batch_size)]\n",
    "            # monitor the reconstruction error\n",
    "            error = 0\n",
    "            for batch in mini_batches:\n",
    "                # perform one step of contrastive divergence (sufficient in practice as per Hinton)\n",
    "                visible_recon, hidden_prob, hidden_recon_last = self.gibbs_sampling(batch)\n",
    "                # update the parameters\n",
    "                self.update_CD(batch, visible_recon, hidden_prob, hidden_recon_last, batch_size, eta, epoch)\n",
    "                error += np.sum((batch-visible_recon)**2)/batch_size\n",
    "                \n",
    "            error = error/(data_size/batch_size)\n",
    "            rec_err[epoch] = error\n",
    "            print('Epoch %s completed. Reconstruction error is %0.2f' % (epoch+1, error))\n",
    "        print('\\nTraining completed.')\n",
    "        \n",
    "        return rec_err\n",
    "        \n",
    "    # update the parameters to maximize the log-likelihood and minimize the reconstruction error\n",
    "    def update_CD(self, batch, visible_recon, hidden_prob, hidden_recon_last, batch_size, eta, epoch):\n",
    "        # compute the gradients for the weights and biases\n",
    "        dw = (np.dot(batch.T, hidden_prob) - np.dot(visible_recon.T, hidden_recon_last))/batch_size\n",
    "        dvb = (np.sum(batch, axis=0) - np.sum(visible_recon, axis=0))/batch_size\n",
    "        dhb = (np.sum(hidden_prob, axis=0) - np.sum(hidden_recon_last, axis=0))/batch_size\n",
    "        \n",
    "        # set momentum and decrease learning rate at the end of training as per Hinton's practical guide\n",
    "        m = 0.5 if epoch < 5 else 0.9\n",
    "        eta = eta/batch_size if epoch > 15 else eta\n",
    "        \n",
    "        # introduce momentum in the update rules\n",
    "        self.w_inc = self.w_inc*m + eta*dw\n",
    "        self.a_inc = self.a_inc*m + eta*dvb\n",
    "        self.b_inc = self.b_inc*m + eta*dhb\n",
    "        \n",
    "        # update the parameters\n",
    "        self.weights += self.w_inc\n",
    "        self.visible_bias += self.a_inc\n",
    "        self.hidden_bias += self.b_inc\n",
    "        \n",
    "    # reconstruct the input vector\n",
    "    def Reconstruct(self, visible, recon_steps):\n",
    "        \n",
    "        V_rec = np.copy(visible)\n",
    "        \n",
    "        for i in range(recon_steps):\n",
    "            p_hidden_given_visible = self.sample_hidden_given_visible(visible)[0]\n",
    "            # sample\n",
    "            hidden_sample = p_hidden_given_visible > np.random.rand(1, self.num_hidden)\n",
    "            V_rec = self.sample_visible_given_hidden(hidden_sample)\n",
    "            \n",
    "        return V_rec\n",
    "        \n",
    "    \n",
    "    # the sigmoid function\n",
    "    def sigmoid(self, z):\n",
    "        sig =  1.0/(1.0 + np.exp(-z))\n",
    "        return sig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fddaedc3",
   "metadata": {},
   "source": [
    "At last, we are ready to train the RBM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "45d28d4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 completed. Reconstruction error is 58.59\n",
      "Epoch 2 completed. Reconstruction error is 42.97\n",
      "Epoch 3 completed. Reconstruction error is 39.36\n",
      "Epoch 4 completed. Reconstruction error is 37.74\n",
      "Epoch 5 completed. Reconstruction error is 36.86\n",
      "Epoch 6 completed. Reconstruction error is 37.05\n",
      "Epoch 7 completed. Reconstruction error is 36.07\n",
      "Epoch 8 completed. Reconstruction error is 35.70\n",
      "Epoch 9 completed. Reconstruction error is 35.41\n",
      "Epoch 10 completed. Reconstruction error is 35.15\n",
      "Epoch 11 completed. Reconstruction error is 34.95\n",
      "Epoch 12 completed. Reconstruction error is 34.83\n",
      "Epoch 13 completed. Reconstruction error is 34.78\n",
      "Epoch 14 completed. Reconstruction error is 34.69\n",
      "Epoch 15 completed. Reconstruction error is 34.62\n",
      "Epoch 16 completed. Reconstruction error is 34.54\n",
      "Epoch 17 completed. Reconstruction error is 33.21\n",
      "Epoch 18 completed. Reconstruction error is 33.07\n",
      "Epoch 19 completed. Reconstruction error is 33.02\n",
      "Epoch 20 completed. Reconstruction error is 33.01\n",
      "\n",
      "Training completed.\n",
      "Training time for 20 epochs, 100 hidden units and learning rate of 0.0125 :--- 300.9391050338745 seconds ---\n"
     ]
    }
   ],
   "source": [
    "rbm = RBM(num_visible, num_hidden)\n",
    "\n",
    "start_time = time.time()\n",
    "rbm.train_RBM(training_data, epochs, batch_size, eta)\n",
    "exec_time = time.time() - start_time\n",
    "print(f\"Training time for {epochs} epochs, {num_hidden} hidden units and learning rate of {eta} :--- {exec_time} seconds ---\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b801a5eb",
   "metadata": {},
   "source": [
    "We should note here that reconstruction error is not representative, but we want to keep track on the training process in terms of convergence. In summary, to count the error and track the training process of an RBM that uses the Contrastive Divergence algorithm, we need to compute the reconstruction error of the model after each training iteration and monitor the trend of the error over time."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4dbd158",
   "metadata": {},
   "source": [
    "### Generate synthetic data with the RBM\n",
    "\n",
    "Now, we will use the RBM to generate synthetic data given samples from the test dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "924c168c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# choose 3 random samples from test dataset\n",
    "sample_1 = test_data[np.random.randint(0, len(test_data)-1)]\n",
    "sample_2 = test_data[np.random.randint(0, len(test_data)-1)]\n",
    "sample_3 = test_data[np.random.randint(0, len(test_data)-1)]\n",
    "# reshape\n",
    "im_1 = np.reshape(sample_1, (28, 28))\n",
    "im_2 = np.reshape(sample_2, (28, 28))\n",
    "im_3 = np.reshape(sample_3, (28, 28))\n",
    "# display\n",
    "fig, ax = plt.subplots(1, 3, figsize=(10,10))\n",
    "ax[0].imshow(im_1, cmap='gray')\n",
    "ax[1].imshow(im_2, cmap='gray')\n",
    "ax[2].imshow(im_3, cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "73fd04fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# reconstruct the images with the RBM\n",
    "rbm_sample_1 = rbm.Reconstruct(sample_1, 5)\n",
    "rbm_sample_2 = rbm.Reconstruct(sample_2, 5)\n",
    "rbm_sample_3 = rbm.Reconstruct(sample_3, 5)\n",
    "\n",
    "# reshape and display\n",
    "rbm_im_1 = np.reshape(rbm_sample_1, (28, 28))\n",
    "rbm_im_2 = np.reshape(rbm_sample_2, (28, 28))\n",
    "rbm_im_3 = np.reshape(rbm_sample_3, (28, 28))\n",
    "fig, ax = plt.subplots(1, 3, figsize=(10,10))\n",
    "ax[0].imshow(rbm_im_1, cmap='gray')\n",
    "ax[1].imshow(rbm_im_2, cmap='gray')\n",
    "ax[2].imshow(rbm_im_3, cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3f88a59",
   "metadata": {},
   "source": [
    "One advantage of using RBMs for synthetic data generation is that they can learn a compressed representation of the input data, which can help to reduce the dimensionality of the data and remove noisy or irrelevant features. This can be particularly useful for applications such as image generation, where the high-dimensional nature of the input data can make it difficult to generate high-quality synthetic images. However, it is important to keep in mind that RBMs are just one of many possible approaches for synthetic data generation and their effectiveness will depend on the specific characteristics of the input data and the requirements of the application. It may be useful to experiment with different generative models and techniques to find the best approach for some particular use case."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4226b730",
   "metadata": {},
   "source": [
    "### Monitor the Reconstruction Error for different hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8b6318b4",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 completed. Reconstruction error is 45.51\n",
      "Epoch 2 completed. Reconstruction error is 38.67\n",
      "Epoch 3 completed. Reconstruction error is 37.72\n",
      "Epoch 4 completed. Reconstruction error is 37.21\n",
      "Epoch 5 completed. Reconstruction error is 36.78\n",
      "Epoch 6 completed. Reconstruction error is 47.87\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_33337/2605302928.py:111: RuntimeWarning: overflow encountered in exp\n",
      "  sig =  1.0/(1.0 + np.exp(-z))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 7 completed. Reconstruction error is 47.63\n",
      "Epoch 8 completed. Reconstruction error is 47.36\n",
      "Epoch 9 completed. Reconstruction error is 46.79\n",
      "Epoch 10 completed. Reconstruction error is 46.77\n",
      "Epoch 11 completed. Reconstruction error is 46.74\n",
      "Epoch 12 completed. Reconstruction error is 46.47\n",
      "Epoch 13 completed. Reconstruction error is 46.49\n",
      "Epoch 14 completed. Reconstruction error is 46.52\n",
      "Epoch 15 completed. Reconstruction error is 46.21\n",
      "Epoch 16 completed. Reconstruction error is 46.15\n",
      "Epoch 17 completed. Reconstruction error is 40.36\n",
      "Epoch 18 completed. Reconstruction error is 39.16\n",
      "Epoch 19 completed. Reconstruction error is 38.81\n",
      "Epoch 20 completed. Reconstruction error is 38.67\n",
      "\n",
      "Training completed.\n",
      "Training time for 20 epochs, 100 hidden units and learning rate of 0.1 :--- 295.48187375068665 seconds ---\n",
      "\n",
      "Epoch 1 completed. Reconstruction error is 48.81\n",
      "Epoch 2 completed. Reconstruction error is 38.46\n",
      "Epoch 3 completed. Reconstruction error is 37.18\n",
      "Epoch 4 completed. Reconstruction error is 36.52\n",
      "Epoch 5 completed. Reconstruction error is 36.17\n",
      "Epoch 6 completed. Reconstruction error is 41.54\n",
      "Epoch 7 completed. Reconstruction error is 41.08\n",
      "Epoch 8 completed. Reconstruction error is 40.84\n",
      "Epoch 9 completed. Reconstruction error is 40.67\n",
      "Epoch 10 completed. Reconstruction error is 40.45\n",
      "Epoch 11 completed. Reconstruction error is 40.39\n",
      "Epoch 12 completed. Reconstruction error is 40.15\n",
      "Epoch 13 completed. Reconstruction error is 39.92\n",
      "Epoch 14 completed. Reconstruction error is 39.94\n",
      "Epoch 15 completed. Reconstruction error is 39.78\n",
      "Epoch 16 completed. Reconstruction error is 39.72\n",
      "Epoch 17 completed. Reconstruction error is 35.48\n",
      "Epoch 18 completed. Reconstruction error is 34.84\n",
      "Epoch 19 completed. Reconstruction error is 34.66\n",
      "Epoch 20 completed. Reconstruction error is 34.54\n",
      "\n",
      "Training completed.\n",
      "Training time for 20 epochs, 100 hidden units and learning rate of 0.05 :--- 295.74547362327576 seconds ---\n",
      "\n",
      "Epoch 1 completed. Reconstruction error is 51.94\n",
      "Epoch 2 completed. Reconstruction error is 39.00\n",
      "Epoch 3 completed. Reconstruction error is 36.80\n",
      "Epoch 4 completed. Reconstruction error is 35.92\n",
      "Epoch 5 completed. Reconstruction error is 35.42\n",
      "Epoch 6 completed. Reconstruction error is 37.51\n",
      "Epoch 7 completed. Reconstruction error is 36.96\n",
      "Epoch 8 completed. Reconstruction error is 36.64\n",
      "Epoch 9 completed. Reconstruction error is 36.49\n",
      "Epoch 10 completed. Reconstruction error is 36.44\n",
      "Epoch 11 completed. Reconstruction error is 36.27\n",
      "Epoch 12 completed. Reconstruction error is 36.21\n",
      "Epoch 13 completed. Reconstruction error is 36.08\n",
      "Epoch 14 completed. Reconstruction error is 35.93\n",
      "Epoch 15 completed. Reconstruction error is 35.82\n",
      "Epoch 16 completed. Reconstruction error is 35.74\n",
      "Epoch 17 completed. Reconstruction error is 33.46\n",
      "Epoch 18 completed. Reconstruction error is 33.18\n",
      "Epoch 19 completed. Reconstruction error is 33.12\n",
      "Epoch 20 completed. Reconstruction error is 33.09\n",
      "\n",
      "Training completed.\n",
      "Training time for 20 epochs, 100 hidden units and learning rate of 0.025 :--- 305.69822573661804 seconds ---\n",
      "\n",
      "Epoch 1 completed. Reconstruction error is 59.29\n",
      "Epoch 2 completed. Reconstruction error is 42.93\n",
      "Epoch 3 completed. Reconstruction error is 39.15\n",
      "Epoch 4 completed. Reconstruction error is 37.58\n",
      "Epoch 5 completed. Reconstruction error is 36.72\n",
      "Epoch 6 completed. Reconstruction error is 37.05\n",
      "Epoch 7 completed. Reconstruction error is 36.30\n",
      "Epoch 8 completed. Reconstruction error is 35.83\n",
      "Epoch 9 completed. Reconstruction error is 35.51\n",
      "Epoch 10 completed. Reconstruction error is 35.22\n",
      "Epoch 11 completed. Reconstruction error is 35.07\n",
      "Epoch 12 completed. Reconstruction error is 35.01\n",
      "Epoch 13 completed. Reconstruction error is 34.85\n",
      "Epoch 14 completed. Reconstruction error is 34.71\n",
      "Epoch 15 completed. Reconstruction error is 34.64\n",
      "Epoch 16 completed. Reconstruction error is 34.51\n",
      "Epoch 17 completed. Reconstruction error is 33.20\n",
      "Epoch 18 completed. Reconstruction error is 33.08\n",
      "Epoch 19 completed. Reconstruction error is 33.04\n",
      "Epoch 20 completed. Reconstruction error is 33.02\n",
      "\n",
      "Training completed.\n",
      "Training time for 20 epochs, 100 hidden units and learning rate of 0.0125 :--- 294.6317446231842 seconds ---\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 100 hidden units\n",
    "eta = [0.1, 0.05, 0.025, 0.0125]\n",
    "error_all = np.zeros((len(eta),epochs))  # 4 tests of 20 epochs each\n",
    "\n",
    "i = 0\n",
    "for lr in eta:\n",
    "        rbm = RBM(784, 100)\n",
    "        start_time = time.time()\n",
    "        error_all[i] = rbm.train_RBM(training_data, epochs, batch_size, lr)\n",
    "        exec_time = time.time() - start_time\n",
    "        print(f\"Training time for 20 epochs, 100 hidden units and learning rate of {lr} :--- {exec_time} seconds ---\")\n",
    "        print()\n",
    "        plt.plot(error_all[i])\n",
    "        i += 1\n",
    "        \n",
    "plt.title(\"RBM with 100 hidden units (Reconstruction Error)\", style='italic')\n",
    "plt.legend(['eta=0.1', 'eta=0.05', 'eta=0.025', 'eta=0.0125'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb2caa5b",
   "metadata": {},
   "source": [
    "As we can see, due to momentum in training, the reconstruction error faces a spike after the 5th epoch. This effect is reduced by decreasing the learning rate by a factor of 2. Also, the decrease of the learning rate at the end of training (after 15 epochs) follows a decrease in error as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4f648f17",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 completed. Reconstruction error is 38.32\n",
      "Epoch 2 completed. Reconstruction error is 31.39\n",
      "Epoch 3 completed. Reconstruction error is 30.37\n",
      "Epoch 4 completed. Reconstruction error is 29.85\n",
      "Epoch 5 completed. Reconstruction error is 29.58\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_33337/2605302928.py:111: RuntimeWarning: overflow encountered in exp\n",
      "  sig =  1.0/(1.0 + np.exp(-z))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 6 completed. Reconstruction error is 46.94\n",
      "Epoch 7 completed. Reconstruction error is 46.04\n",
      "Epoch 8 completed. Reconstruction error is 45.21\n",
      "Epoch 9 completed. Reconstruction error is 44.81\n",
      "Epoch 10 completed. Reconstruction error is 44.21\n",
      "Epoch 11 completed. Reconstruction error is 43.94\n",
      "Epoch 12 completed. Reconstruction error is 43.83\n",
      "Epoch 13 completed. Reconstruction error is 43.69\n",
      "Epoch 14 completed. Reconstruction error is 43.38\n",
      "Epoch 15 completed. Reconstruction error is 43.57\n",
      "Epoch 16 completed. Reconstruction error is 43.49\n",
      "Epoch 17 completed. Reconstruction error is 36.83\n",
      "Epoch 18 completed. Reconstruction error is 34.68\n",
      "Epoch 19 completed. Reconstruction error is 33.78\n",
      "Epoch 20 completed. Reconstruction error is 33.22\n",
      "\n",
      "Training completed.\n",
      "Training time for 20 epochs, 200 hidden units and learning rate of 0.1 :--- 539.7165448665619 seconds ---\n",
      "\n",
      "Epoch 1 completed. Reconstruction error is 39.96\n",
      "Epoch 2 completed. Reconstruction error is 30.05\n",
      "Epoch 3 completed. Reconstruction error is 28.59\n",
      "Epoch 4 completed. Reconstruction error is 27.90\n",
      "Epoch 5 completed. Reconstruction error is 27.45\n",
      "Epoch 6 completed. Reconstruction error is 37.78\n",
      "Epoch 7 completed. Reconstruction error is 37.52\n",
      "Epoch 8 completed. Reconstruction error is 37.13\n",
      "Epoch 9 completed. Reconstruction error is 36.71\n",
      "Epoch 10 completed. Reconstruction error is 36.53\n",
      "Epoch 11 completed. Reconstruction error is 36.15\n",
      "Epoch 12 completed. Reconstruction error is 35.95\n",
      "Epoch 13 completed. Reconstruction error is 35.75\n",
      "Epoch 14 completed. Reconstruction error is 35.69\n",
      "Epoch 15 completed. Reconstruction error is 35.57\n",
      "Epoch 16 completed. Reconstruction error is 35.40\n",
      "Epoch 17 completed. Reconstruction error is 30.49\n",
      "Epoch 18 completed. Reconstruction error is 28.98\n",
      "Epoch 19 completed. Reconstruction error is 28.40\n",
      "Epoch 20 completed. Reconstruction error is 28.05\n",
      "\n",
      "Training completed.\n",
      "Training time for 20 epochs, 200 hidden units and learning rate of 0.05 :--- 537.8568480014801 seconds ---\n",
      "\n",
      "Epoch 1 completed. Reconstruction error is 43.18\n",
      "Epoch 2 completed. Reconstruction error is 30.71\n",
      "Epoch 3 completed. Reconstruction error is 28.43\n",
      "Epoch 4 completed. Reconstruction error is 27.35\n",
      "Epoch 5 completed. Reconstruction error is 26.73\n",
      "Epoch 6 completed. Reconstruction error is 31.01\n",
      "Epoch 7 completed. Reconstruction error is 30.54\n",
      "Epoch 8 completed. Reconstruction error is 30.15\n",
      "Epoch 9 completed. Reconstruction error is 29.91\n",
      "Epoch 10 completed. Reconstruction error is 29.66\n",
      "Epoch 11 completed. Reconstruction error is 29.54\n",
      "Epoch 12 completed. Reconstruction error is 29.43\n",
      "Epoch 13 completed. Reconstruction error is 29.34\n",
      "Epoch 14 completed. Reconstruction error is 29.24\n",
      "Epoch 15 completed. Reconstruction error is 29.16\n",
      "Epoch 16 completed. Reconstruction error is 29.09\n",
      "Epoch 17 completed. Reconstruction error is 25.33\n",
      "Epoch 18 completed. Reconstruction error is 24.77\n",
      "Epoch 19 completed. Reconstruction error is 24.57\n",
      "Epoch 20 completed. Reconstruction error is 24.46\n",
      "\n",
      "Training completed.\n",
      "Training time for 20 epochs, 200 hidden units and learning rate of 0.025 :--- 531.0911803245544 seconds ---\n",
      "\n",
      "Epoch 1 completed. Reconstruction error is 48.52\n",
      "Epoch 2 completed. Reconstruction error is 33.43\n",
      "Epoch 3 completed. Reconstruction error is 30.14\n",
      "Epoch 4 completed. Reconstruction error is 28.57\n",
      "Epoch 5 completed. Reconstruction error is 27.60\n",
      "Epoch 6 completed. Reconstruction error is 28.70\n",
      "Epoch 7 completed. Reconstruction error is 27.71\n",
      "Epoch 8 completed. Reconstruction error is 27.20\n",
      "Epoch 9 completed. Reconstruction error is 26.90\n",
      "Epoch 10 completed. Reconstruction error is 26.67\n",
      "Epoch 11 completed. Reconstruction error is 26.51\n",
      "Epoch 12 completed. Reconstruction error is 26.34\n",
      "Epoch 13 completed. Reconstruction error is 26.23\n",
      "Epoch 14 completed. Reconstruction error is 26.12\n",
      "Epoch 15 completed. Reconstruction error is 26.00\n",
      "Epoch 16 completed. Reconstruction error is 25.90\n",
      "Epoch 17 completed. Reconstruction error is 23.73\n",
      "Epoch 18 completed. Reconstruction error is 23.51\n",
      "Epoch 19 completed. Reconstruction error is 23.42\n",
      "Epoch 20 completed. Reconstruction error is 23.37\n",
      "\n",
      "Training completed.\n",
      "Training time for 20 epochs, 200 hidden units and learning rate of 0.0125 :--- 532.9121761322021 seconds ---\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 200 hidden units\n",
    "eta = [0.1, 0.05, 0.025, 0.0125]\n",
    "error_all = np.zeros((len(eta),epochs))  # 4 tests of 20 epochs each\n",
    "\n",
    "i = 0\n",
    "for lr in eta:\n",
    "        rbm = RBM(784, 200)\n",
    "        start_time = time.time()\n",
    "        error_all[i] = rbm.train_RBM(training_data, epochs, batch_size, lr)\n",
    "        exec_time = time.time() - start_time\n",
    "        print(f\"Training time for 20 epochs, 200 hidden units and learning rate of {lr} :--- {exec_time} seconds ---\")\n",
    "        print()\n",
    "        plt.plot(error_all[i])\n",
    "        i += 1\n",
    "        \n",
    "plt.title(\"RBM with 200 hidden units (Reconstruction Error)\", style='italic')\n",
    "plt.legend(['eta=0.1', 'eta=0.05', 'eta=0.025', 'eta=0.0125'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d29b711",
   "metadata": {},
   "source": [
    "### Differences between MNIST and Fashion-MNIST\n",
    "\n",
    "One key difference between MNIST and Fashion-MNIST is the complexity of the classification task. While MNIST consists of simple, uniform images of handwritten digits, Fashion-MNIST includes more diverse and complex images of clothing and accessories, with variations in texture, shape, and style. This makes the task of classifying the images in Fashion-MNIST more challenging than the task in MNIST.\n",
    "\n",
    "Another difference between the two datasets is their relevance to real-world applications. MNIST has been used for decades as a standard benchmark for image classification tasks, but its practical applications are limited. Fashion-MNIST, on the other hand, was designed to be a more realistic and challenging dataset that better reflects the types of images encountered in real-world computer vision applications, such as e-commerce and fashion recommendation systems."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "ml_venv",
   "language": "python",
   "name": "ml_venv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}