PY580_Notebook17_Restricted_Boltzmann_Machines.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notebook 17: Energy-based Generative Models for MNIST\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learning Goal\n",
    "The goal of this notebook is to familiarize readers with various energy-based generative models including: Restricted Boltzmann Machines (RBMs) with Gaussian and Bernoulli units, Deep Boltzmann Machines (DBMs), as well as techniques for training these model including contrastive divergence (CD) and persistent constrastive divergence (PCD). We will also discuss how to generate new examples (commonly called fantasy particles in the ML literature). The notebook also introduces the [Paysage](https://github.com/drckf/paysage) package from [UnLearn.AI](https://unlearn.ai/) for quickly building and training these models..\n",
    "\n",
    "## Overview\n",
    "In this notebook, we study the MNIST dataset using generative models. \n",
    "\n",
    "Let us adopt a different perspective on the MNIST dataset. Generative models, as the name suggests, are useful to generate brand new data (images) by learning how to imitate the ones from a given data set. If you wish, they can be regarded as a kind of \"creative ML\". This is achieved by extracting/learning a set of features which represent the backbone of the entire data and are thus definitive for the particular dataset. These features are encoded in the weights of the model. \n",
    "\n",
    "Mathematically speaking, generative models are designed and trained to learn an approximation for the probability distribution that generated the data. Intuitively, this task is much more complex and sophisticated than the image recognition task. Therefore, we shall approach the problem in a number of steps of increasing complexity. For a more detailed discussion on the theory, we invite the reader to check out Secs. XV and XVI of the review.\n",
    "\n",
    "Below, we analyze four different generative models: the Hopfield Model, a Restricted Boltzmann Machine (RBM), a regularized RMB with sparse weights, and a Deep Boltzmann Machine (DBM). In all these cases, we first set up and train the models. After that, we compare the results. Last, we open up the black box of each model and visualise a set of features it learned. \n",
    "\n",
    "## Setting up Paysage\n",
    "\n",
    "In this notebook, we use an open-source `python` package for energy-based models, called [paysage](https://github.com/drckf/paysage). Paysage requires `python>3.5`; we recommend using the package with an [Anaconda](https://www.continuum.io/downloads) environment.\n",
    "\n",
    "To install paysage: \n",
    "\n",
    "* clone or download the [github repo](https://github.com/drckf/paysage)\n",
    "* activate an Anaconda3 environment\n",
    "* navigate to the directory which contains the paysage files\n",
    "* and execute\n",
    "```\n",
    "pip install .\n",
    "```\n",
    "\n",
    "Documentation for paysage is available under [https://github.com/drckf/paysage/tree/master/docs](https://github.com/drckf/paysage/tree/master/docs).\n",
    "\n",
    "By default, computations in paysage are performed using `numpy`/`numexpr`/`numba` on the CPU. If you have installed [PyTorch](https://pytorch.org), then you can switch to the `pytorch` backend by changing the setting in `paysage/backends/config.json` to `pytorch`. \n",
    "\n",
    "Let us set up the required packages for this notebook by importing paysage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "import os\n",
    "import paysage\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# for Boltzmann machines\n",
    "from paysage import preprocess as pre\n",
    "from paysage.layers import BernoulliLayer, GaussianLayer\n",
    "from paysage.models import BoltzmannMachine\n",
    "from paysage import batch\n",
    "from paysage import fit\n",
    "from paysage import optimizers\n",
    "from paysage import samplers\n",
    "from paysage import backends as be\n",
    "from paysage import schedules\n",
    "from paysage import penalties as pen\n",
    "\n",
    "# fix random seed to ensure deterministic behavior\n",
    "np.random.seed(137)\n",
    "be.set_seed(137) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Obtaining the MNIST dataset\n",
    "\n",
    "As we mentioned in the introduction, we use the MNIST dataset of handwritten digits to study the Hopfield model and various variants of RBMs. \n",
    "\n",
    "The MNIST dataset comprises $70000$ handwritten digits, each of which comes in a square image, divided into a $28\\times 28$ pixel grid. Every pixel can take on $256$ nuances of the grey colour, interpolating between white and black, and hence each data point assumes any value in the set $\\{0,1,\\dots,255\\}$. There are $10$ categories in the problem, corresponding to the ten digits. In previous notebooks, we formulated a classification task for the MNIST dataset, and studied it using discriminative supervised learning: Logistic Regression and Deep Neural Networks. \n",
    "\n",
    "\n",
    "This dataset can be fetched using paysage from the web as an `HDF5` file. For this, you should\n",
    "\n",
    "* navigate to the directory in which you cloned/downloaded paysage\n",
    "* navigate further into the `/examples/mnist/` directory which contains the file `download_mnist.py`.\n",
    "* from the terminal, run the command \n",
    "```\n",
    "python3 /examples/mnist/download_mnist.py\n",
    "```\n",
    "\n",
    "This file contains keys `train/images`, `train/labels`, `test/images`, and `test/labels` and is compressed to about 15 Mb in size.\n",
    "\n",
    "As our first step, we will set up the paths to the data and shuffle the dataset. The shuffled dataset will not be compressed (for faster reading during training) so it will be about 56 Mb in size.\n",
    "\n",
    "_Why shuffle the data?_ - Training with stochastic gradient descent means we will be using small minibatches of data (maybe 50 examples) to compute the gradient at each step. If the data have an order, then the estimates for the gradients computed from the minibatches will be biased. Shuffling the data ensures that the gradient estimates are unbiased (though still noisy)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "path to mnist data:\n",
      "/Users/chinghao/Downloads/paysage-master/examples/mnist/mnist.h5\n"
     ]
    }
   ],
   "source": [
    "paysage_path = os.path.dirname(os.path.dirname(paysage.__file__))\n",
    "mnist_path = os.path.join(paysage_path, \"examples\", \"mnist\", \"mnist.h5\")\n",
    "shuffled_mnist_path = os.path.join(paysage_path, \"examples\", \"mnist\", \"shuffled_mnist.h5\")\n",
    "\n",
    "print(\"path to mnist data:\")\n",
    "print(mnist_path)\n",
    "\n",
    "if not os.path.exists(mnist_path):\n",
    "    raise IOError(\"{} does not exist. run mnist/download_mnist.py to fetch from the web\".format(mnist_path))\n",
    "    \n",
    "if not os.path.exists(shuffled_mnist_path):\n",
    "    batch.DataShuffler(mnist_path, shuffled_mnist_path, complevel=0).shuffle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Processing the Data\n",
    "\n",
    "Next, we create a `data` generator, which splits the data into a training and validation sets, and separates them into minibatches of size `batch_size`. Before we begin training, we set `data` into training mode. \n",
    "\n",
    "To monitor the progress of performance metrics during training, we define the variable `performance` which tells Paysage to measure the reconstruction error from the validation set. Possible metrics include the reconstruction error (used in this example) and metrics related to difference in energy of random samples and samples from the model (see [`metrics.md`](https://github.com/drckf/paysage/blob/master/docs/metrics.md) in Paysage documentation for a complete list)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:7: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  import sys\n"
     ]
    }
   ],
   "source": [
    "##### set up minibatch data generator\n",
    "# batch size\n",
    "batch_size=100 \n",
    "transform = pre.Transformation(pre.binarize_color)\n",
    "\n",
    "# create data generator object with minibathces\n",
    "samples = be.float_tensor(pd.read_hdf(shuffled_mnist_path, key='train/images').value)\n",
    "data = batch.in_memory_batch(samples, batch_size, train_fraction=0.95, transform=transform)\n",
    "\n",
    "# reset the data generator in training mode\n",
    "data.reset_generator(mode='train') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setting up a Hopfield Model\n",
    "\n",
    "Having loaded and preprocessed the data, we now move on to construct a `hopfield` model. To do this, we use the `Model` class and with a visible `BernoulliLayer` and a hidden `GaussianLayer`. Note that the visible layer has the same size as the input data points, which is can be read off `data.ncols`. The number of hidden units is `num_hidden_units`. We also set the mean and variance of the Gaussian layer to zero and unity, respectively (the notation here is inspired by the terminology in Variational Auto Encoders).\n",
    "\n",
    "We choose to train the model with the `Adam` optimizer. To ensure convergence, we attenuate the `learning_rate` hyperparameter according to a `PowerLawDecay` schedule: `learning_rate`$(t)$ =`initial`$/(1 +$ `coefficient`$\\;\\times\\; t)$. It will prove convenient to define the function `Adam_optimizer()` for this purpose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "##### create hopfield model\n",
    "# hidden units\n",
    "num_hidden_units=200 \n",
    "\n",
    "# set up the model\n",
    "vis_layer = BernoulliLayer(data.ncols)\n",
    "hid_layer = GaussianLayer(num_hidden_units)\n",
    "hopfield = BoltzmannMachine([vis_layer, hid_layer])\n",
    "\n",
    "# set mean and standard deviation of hidden layer to to 0 and 1, respectively\n",
    "hopfield.layers[1].set_fixed_params(['loc', 'log_var'])\n",
    "\n",
    "# set up an optimizer method (ADAM in this case)\n",
    "def ADAM_optimizer(initial,coefficient):\n",
    "\t# define learning rate attenuation schedule\n",
    "\tlearning_rate=schedules.PowerLawDecay(initial=initial,coefficient=coefficient)\n",
    "\t# return optimizer object\n",
    "\treturn optimizers.ADAM(stepsize=learning_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compiling and Training a Model in Paysage\n",
    "\n",
    "Next, we have compile the model. First, we initialize a `model` using the `initialize` function attribute which accepts the `data` as a required argument. We choose the initialization routine `glorot`, see discussion in review. Second, we define an optimizer calling the function `Adam_optimizer()` defined above, and store the object under the name `opt`. To define a Monte Carlo `sampler`, we use the method `from_batch` of the `SequentialMC` class, parsing the `model` and the `data`. Last, we create an `SGD` object called `trainer` to train the model using Persistent Contrastive Divergence (`pcd`) with a fixed number of `monte_carlo_steps`. We can also `monitor` the reconstruction error during training. Last, we train the model in epochs (see variable `nim_epochs`), calling the `train()` method of `trainer`. These steps are universal for shallow generative `model`'s, and it is convenient to combine them in the function `train_model()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before training:\n",
      "-ReconstructionError: 1.203098\n",
      "-EnergyCoefficient: 0.134485\n",
      "-HeatCapacity: 0.434479\n",
      "-WeightSparsity: 0.335712\n",
      "-WeightSquare: 1.588543\n",
      "-KLDivergence: 0.188799\n",
      "-ReverseKLDivergence: -0.036247\n",
      "\n",
      "End of epoch 1: \n",
      "Time elapsed 5.769s\n",
      "-ReconstructionError: 0.758059\n",
      "-EnergyCoefficient: 0.271930\n",
      "-HeatCapacity: 8.722163\n",
      "-WeightSparsity: 0.268762\n",
      "-WeightSquare: 2.355603\n",
      "-KLDivergence: 0.089433\n",
      "-ReverseKLDivergence: 0.153994\n",
      "\n",
      "End of epoch 2: \n",
      "Time elapsed 5.785s\n",
      "-ReconstructionError: 0.717784\n",
      "-EnergyCoefficient: 0.290698\n",
      "-HeatCapacity: 12.103565\n",
      "-WeightSparsity: 0.268668\n",
      "-WeightSquare: 2.623842\n",
      "-KLDivergence: 0.077823\n",
      "-ReverseKLDivergence: 0.192197\n",
      "\n",
      "End of epoch 3: \n",
      "Time elapsed 5.529s\n",
      "-ReconstructionError: 0.720571\n",
      "-EnergyCoefficient: 0.355613\n",
      "-HeatCapacity: 9.184643\n",
      "-WeightSparsity: 0.267966\n",
      "-WeightSquare: 2.789534\n",
      "-KLDivergence: 0.071486\n",
      "-ReverseKLDivergence: 0.328846\n",
      "\n",
      "End of epoch 4: \n",
      "Time elapsed 5.623s\n",
      "-ReconstructionError: 0.721592\n",
      "-EnergyCoefficient: 0.315879\n",
      "-HeatCapacity: 19.097582\n",
      "-WeightSparsity: 0.267072\n",
      "-WeightSquare: 2.881694\n",
      "-KLDivergence: 0.089170\n",
      "-ReverseKLDivergence: 0.226370\n",
      "\n",
      "End of epoch 5: \n",
      "Time elapsed 5.985s\n",
      "-ReconstructionError: 0.731511\n",
      "-EnergyCoefficient: 0.352591\n",
      "-HeatCapacity: 12.398974\n",
      "-WeightSparsity: 0.270751\n",
      "-WeightSquare: 2.860990\n",
      "-KLDivergence: 0.101515\n",
      "-ReverseKLDivergence: 0.312168\n",
      "\n",
      "End of epoch 6: \n",
      "Time elapsed 5.66s\n",
      "-ReconstructionError: 0.766730\n",
      "-EnergyCoefficient: 0.329614\n",
      "-HeatCapacity: 12.116742\n",
      "-WeightSparsity: 0.278617\n",
      "-WeightSquare: 2.792415\n",
      "-KLDivergence: 0.058859\n",
      "-ReverseKLDivergence: 0.252365\n",
      "\n",
      "End of epoch 7: \n",
      "Time elapsed 5.785s\n",
      "-ReconstructionError: 0.722264\n",
      "-EnergyCoefficient: 0.353819\n",
      "-HeatCapacity: 8.638835\n",
      "-WeightSparsity: 0.279320\n",
      "-WeightSquare: 2.912473\n",
      "-KLDivergence: 0.062427\n",
      "-ReverseKLDivergence: 0.300098\n",
      "\n",
      "End of epoch 8: \n",
      "Time elapsed 5.471s\n",
      "-ReconstructionError: 0.736371\n",
      "-EnergyCoefficient: 0.310364\n",
      "-HeatCapacity: 154.251839\n",
      "-WeightSparsity: 0.276663\n",
      "-WeightSquare: 3.021360\n",
      "-KLDivergence: 0.082398\n",
      "-ReverseKLDivergence: 0.249388\n",
      "\n",
      "End of epoch 9: \n",
      "Time elapsed 5.657s\n",
      "-ReconstructionError: 0.715077\n",
      "-EnergyCoefficient: 0.357051\n",
      "-HeatCapacity: 45.662843\n",
      "-WeightSparsity: 0.274935\n",
      "-WeightSquare: 3.170220\n",
      "-KLDivergence: 0.072203\n",
      "-ReverseKLDivergence: 0.402410\n",
      "\n",
      "End of epoch 10: \n",
      "Time elapsed 5.924s\n",
      "-ReconstructionError: 0.701699\n",
      "-EnergyCoefficient: 0.213532\n",
      "-HeatCapacity: 44.744286\n",
      "-WeightSparsity: 0.267844\n",
      "-WeightSquare: 3.424128\n",
      "-KLDivergence: 0.042195\n",
      "-ReverseKLDivergence: 0.176381\n",
      "\n",
      "End of epoch 11: \n",
      "Time elapsed 5.874s\n",
      "-ReconstructionError: 0.704685\n",
      "-EnergyCoefficient: 0.287322\n",
      "-HeatCapacity: 49.121368\n",
      "-WeightSparsity: 0.261188\n",
      "-WeightSquare: 3.559100\n",
      "-KLDivergence: 0.039975\n",
      "-ReverseKLDivergence: 0.235038\n",
      "\n",
      "End of epoch 12: \n",
      "Time elapsed 5.414s\n",
      "-ReconstructionError: 0.704191\n",
      "-EnergyCoefficient: 0.335872\n",
      "-HeatCapacity: 70.598681\n",
      "-WeightSparsity: 0.257006\n",
      "-WeightSquare: 3.789706\n",
      "-KLDivergence: 0.086966\n",
      "-ReverseKLDivergence: 0.332300\n",
      "\n",
      "End of epoch 13: \n",
      "Time elapsed 5.503s\n",
      "-ReconstructionError: 0.691235\n",
      "-EnergyCoefficient: 0.290370\n",
      "-HeatCapacity: 21.146751\n",
      "-WeightSparsity: 0.254605\n",
      "-WeightSquare: 4.006200\n",
      "-KLDivergence: 0.028466\n",
      "-ReverseKLDivergence: 0.208005\n",
      "\n",
      "End of epoch 14: \n",
      "Time elapsed 5.538s\n",
      "-ReconstructionError: 0.691635\n",
      "-EnergyCoefficient: 0.324749\n",
      "-HeatCapacity: 57.623025\n",
      "-WeightSparsity: 0.254884\n",
      "-WeightSquare: 4.318763\n",
      "-KLDivergence: 0.024234\n",
      "-ReverseKLDivergence: 0.316771\n",
      "\n",
      "End of epoch 15: \n",
      "Time elapsed 6.203s\n",
      "-ReconstructionError: 0.688565\n",
      "-EnergyCoefficient: 0.370633\n",
      "-HeatCapacity: 38.042551\n",
      "-WeightSparsity: 0.256465\n",
      "-WeightSquare: 4.470937\n",
      "-KLDivergence: 0.109225\n",
      "-ReverseKLDivergence: 0.387763\n",
      "\n",
      "End of epoch 16: \n",
      "Time elapsed 5.797s\n",
      "-ReconstructionError: 0.668726\n",
      "-EnergyCoefficient: 0.300863\n",
      "-HeatCapacity: 259.275070\n",
      "-WeightSparsity: 0.259555\n",
      "-WeightSquare: 4.877840\n",
      "-KLDivergence: 0.046502\n",
      "-ReverseKLDivergence: 0.313053\n",
      "\n",
      "End of epoch 17: \n",
      "Time elapsed 6.329s\n",
      "-ReconstructionError: 0.698139\n",
      "-EnergyCoefficient: 0.503270\n",
      "-HeatCapacity: 439.002197\n",
      "-WeightSparsity: 0.264087\n",
      "-WeightSquare: 5.104922\n",
      "-KLDivergence: 0.169157\n",
      "-ReverseKLDivergence: 0.636722\n",
      "\n",
      "End of epoch 18: \n",
      "Time elapsed 6.002s\n",
      "-ReconstructionError: 0.687114\n",
      "-EnergyCoefficient: 0.279782\n",
      "-HeatCapacity: 59.622955\n",
      "-WeightSparsity: 0.265842\n",
      "-WeightSquare: 5.337249\n",
      "-KLDivergence: 0.029801\n",
      "-ReverseKLDivergence: 0.267772\n",
      "\n",
      "End of epoch 19: \n",
      "Time elapsed 9.392s\n",
      "-ReconstructionError: 0.675484\n",
      "-EnergyCoefficient: 0.308026\n",
      "-HeatCapacity: 496.223302\n",
      "-WeightSparsity: 0.274207\n",
      "-WeightSquare: 5.625677\n",
      "-KLDivergence: 0.077853\n",
      "-ReverseKLDivergence: 0.308562\n",
      "\n",
      "End of epoch 20: \n",
      "Time elapsed 5.745s\n",
      "-ReconstructionError: 0.666614\n",
      "-EnergyCoefficient: 0.314069\n",
      "-HeatCapacity: 407.979512\n",
      "-WeightSparsity: 0.267616\n",
      "-WeightSquare: 6.095773\n",
      "-KLDivergence: 0.087877\n",
      "-ReverseKLDivergence: 0.308343\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# define function to compile and train model\n",
    "num_epochs=20 # training epochs\n",
    "monte_carlo_steps=1 # number of MC sampling steps\n",
    "def train_model(model,num_epochs,monte_carlo_steps):\n",
    "        # make a simple guess for the initial parameters of the model\n",
    "        model.initialize(data,method='glorot_normal')\n",
    "        # set optimizer\n",
    "        opt=ADAM_optimizer(1E-2,1.0)\n",
    "        trainer = fit.SGD(model, data)\n",
    "        trainer.train(opt, num_epochs, method=fit.pcd, mcsteps=monte_carlo_steps)\n",
    "# train hopfield model\n",
    "train_model(hopfield,num_epochs,monte_carlo_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More Generative Models\n",
    "\n",
    "We can easily create a Bernoulli RBM and train it using the functions defined above as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before training:\n",
      "-ReconstructionError: 1.224468\n",
      "-EnergyCoefficient: 0.130849\n",
      "-HeatCapacity: 0.310575\n",
      "-WeightSparsity: 0.335764\n",
      "-WeightSquare: 1.586147\n",
      "-KLDivergence: 0.172399\n",
      "-ReverseKLDivergence: -0.036571\n",
      "\n",
      "End of epoch 1: \n",
      "Time elapsed 4.522s\n",
      "-ReconstructionError: 0.883955\n",
      "-EnergyCoefficient: 0.332970\n",
      "-HeatCapacity: 0.419587\n",
      "-WeightSparsity: 0.228966\n",
      "-WeightSquare: 27.294800\n",
      "-KLDivergence: 0.141439\n",
      "-ReverseKLDivergence: 0.220725\n",
      "\n",
      "End of epoch 2: \n",
      "Time elapsed 4.698s\n",
      "-ReconstructionError: 0.811407\n",
      "-EnergyCoefficient: 0.321183\n",
      "-HeatCapacity: 0.880261\n",
      "-WeightSparsity: 0.228917\n",
      "-WeightSquare: 48.228872\n",
      "-KLDivergence: 0.054885\n",
      "-ReverseKLDivergence: 0.255241\n",
      "\n",
      "End of epoch 3: \n",
      "Time elapsed 4.524s\n",
      "-ReconstructionError: 0.772367\n",
      "-EnergyCoefficient: 0.358062\n",
      "-HeatCapacity: 0.704555\n",
      "-WeightSparsity: 0.227952\n",
      "-WeightSquare: 68.845010\n",
      "-KLDivergence: 0.097184\n",
      "-ReverseKLDivergence: 0.276903\n",
      "\n",
      "End of epoch 4: \n",
      "Time elapsed 4.394s\n",
      "-ReconstructionError: 0.740070\n",
      "-EnergyCoefficient: 0.308440\n",
      "-HeatCapacity: 1.553747\n",
      "-WeightSparsity: 0.222856\n",
      "-WeightSquare: 92.983086\n",
      "-KLDivergence: 0.066805\n",
      "-ReverseKLDivergence: 0.251889\n",
      "\n",
      "End of epoch 5: \n",
      "Time elapsed 4.49s\n",
      "-ReconstructionError: 0.731708\n",
      "-EnergyCoefficient: 0.320784\n",
      "-HeatCapacity: 0.859078\n",
      "-WeightSparsity: 0.219865\n",
      "-WeightSquare: 119.025088\n",
      "-KLDivergence: 0.090319\n",
      "-ReverseKLDivergence: 0.275634\n",
      "\n",
      "End of epoch 6: \n",
      "Time elapsed 4.493s\n",
      "-ReconstructionError: 0.713038\n",
      "-EnergyCoefficient: 0.305011\n",
      "-HeatCapacity: 2.768552\n",
      "-WeightSparsity: 0.217180\n",
      "-WeightSquare: 142.648643\n",
      "-KLDivergence: 0.069115\n",
      "-ReverseKLDivergence: 0.265705\n",
      "\n",
      "End of epoch 7: \n",
      "Time elapsed 4.408s\n",
      "-ReconstructionError: 0.688988\n",
      "-EnergyCoefficient: 0.284860\n",
      "-HeatCapacity: 1.013125\n",
      "-WeightSparsity: 0.214577\n",
      "-WeightSquare: 170.406582\n",
      "-KLDivergence: 0.073234\n",
      "-ReverseKLDivergence: 0.237190\n",
      "\n",
      "End of epoch 8: \n",
      "Time elapsed 4.385s\n",
      "-ReconstructionError: 0.674123\n",
      "-EnergyCoefficient: 0.308595\n",
      "-HeatCapacity: 1.589566\n",
      "-WeightSparsity: 0.210311\n",
      "-WeightSquare: 199.337539\n",
      "-KLDivergence: 0.065292\n",
      "-ReverseKLDivergence: 0.267515\n",
      "\n",
      "End of epoch 9: \n",
      "Time elapsed 4.426s\n",
      "-ReconstructionError: 0.664312\n",
      "-EnergyCoefficient: 0.236081\n",
      "-HeatCapacity: 1.614356\n",
      "-WeightSparsity: 0.207115\n",
      "-WeightSquare: 227.100352\n",
      "-KLDivergence: 0.044944\n",
      "-ReverseKLDivergence: 0.187422\n",
      "\n",
      "End of epoch 10: \n",
      "Time elapsed 4.405s\n",
      "-ReconstructionError: 0.661648\n",
      "-EnergyCoefficient: 0.279143\n",
      "-HeatCapacity: 0.950736\n",
      "-WeightSparsity: 0.202672\n",
      "-WeightSquare: 257.587344\n",
      "-KLDivergence: 0.053314\n",
      "-ReverseKLDivergence: 0.215839\n",
      "\n",
      "End of epoch 11: \n",
      "Time elapsed 4.483s\n",
      "-ReconstructionError: 0.645672\n",
      "-EnergyCoefficient: 0.295663\n",
      "-HeatCapacity: 1.578886\n",
      "-WeightSparsity: 0.198769\n",
      "-WeightSquare: 291.084902\n",
      "-KLDivergence: 0.077674\n",
      "-ReverseKLDivergence: 0.243625\n",
      "\n",
      "End of epoch 12: \n",
      "Time elapsed 4.416s\n",
      "-ReconstructionError: 0.648426\n",
      "-EnergyCoefficient: 0.303596\n",
      "-HeatCapacity: 1.018800\n",
      "-WeightSparsity: 0.195713\n",
      "-WeightSquare: 321.116816\n",
      "-KLDivergence: 0.051571\n",
      "-ReverseKLDivergence: 0.248795\n",
      "\n",
      "End of epoch 13: \n",
      "Time elapsed 4.457s\n",
      "-ReconstructionError: 0.633800\n",
      "-EnergyCoefficient: 0.310184\n",
      "-HeatCapacity: 1.355048\n",
      "-WeightSparsity: 0.193115\n",
      "-WeightSquare: 357.970937\n",
      "-KLDivergence: 0.074406\n",
      "-ReverseKLDivergence: 0.263160\n",
      "\n",
      "End of epoch 14: \n",
      "Time elapsed 4.438s\n",
      "-ReconstructionError: 0.646390\n",
      "-EnergyCoefficient: 0.327606\n",
      "-HeatCapacity: 0.869651\n",
      "-WeightSparsity: 0.191093\n",
      "-WeightSquare: 389.334883\n",
      "-KLDivergence: 0.060235\n",
      "-ReverseKLDivergence: 0.296907\n",
      "\n",
      "End of epoch 15: \n",
      "Time elapsed 4.474s\n",
      "-ReconstructionError: 0.627265\n",
      "-EnergyCoefficient: 0.329762\n",
      "-HeatCapacity: 1.396677\n",
      "-WeightSparsity: 0.188078\n",
      "-WeightSquare: 420.165898\n",
      "-KLDivergence: 0.058524\n",
      "-ReverseKLDivergence: 0.325603\n",
      "\n",
      "End of epoch 16: \n",
      "Time elapsed 4.478s\n",
      "-ReconstructionError: 0.619721\n",
      "-EnergyCoefficient: 0.282050\n",
      "-HeatCapacity: 1.025812\n",
      "-WeightSparsity: 0.184616\n",
      "-WeightSquare: 451.747227\n",
      "-KLDivergence: 0.044132\n",
      "-ReverseKLDivergence: 0.246989\n",
      "\n",
      "End of epoch 17: \n",
      "Time elapsed 4.473s\n",
      "-ReconstructionError: 0.614058\n",
      "-EnergyCoefficient: 0.250938\n",
      "-HeatCapacity: 1.339757\n",
      "-WeightSparsity: 0.181705\n",
      "-WeightSquare: 481.926836\n",
      "-KLDivergence: 0.050620\n",
      "-ReverseKLDivergence: 0.185795\n",
      "\n",
      "End of epoch 18: \n",
      "Time elapsed 4.466s\n",
      "-ReconstructionError: 0.611834\n",
      "-EnergyCoefficient: 0.311016\n",
      "-HeatCapacity: 2.963359\n",
      "-WeightSparsity: 0.179652\n",
      "-WeightSquare: 515.877813\n",
      "-KLDivergence: 0.055627\n",
      "-ReverseKLDivergence: 0.253775\n",
      "\n",
      "End of epoch 19: \n",
      "Time elapsed 4.491s\n",
      "-ReconstructionError: 0.607172\n",
      "-EnergyCoefficient: 0.227891\n",
      "-HeatCapacity: 2.129426\n",
      "-WeightSparsity: 0.177144\n",
      "-WeightSquare: 547.434766\n",
      "-KLDivergence: 0.062796\n",
      "-ReverseKLDivergence: 0.129485\n",
      "\n",
      "End of epoch 20: \n",
      "Time elapsed 4.527s\n",
      "-ReconstructionError: 0.606728\n",
      "-EnergyCoefficient: 0.238340\n",
      "-HeatCapacity: 2.024708\n",
      "-WeightSparsity: 0.174810\n",
      "-WeightSquare: 577.939414\n",
      "-KLDivergence: 0.041814\n",
      "-ReverseKLDivergence: 0.179241\n",
      "\n"
     ]
    }
   ],
   "source": [
    "##### Bernoulli RBM\n",
    "vis_layer = BernoulliLayer(data.ncols)\n",
    "hid_layer = BernoulliLayer(num_hidden_units)\n",
    "rbm = BoltzmannMachine([vis_layer, hid_layer])\n",
    "\n",
    "# train Bernoulli RBM\n",
    "train_model(rbm,num_epochs,monte_carlo_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constructing a Bernoulli RBM with L1 regularization is also straightforward in Paysage, using the `add_penalty` method which accepts a dictionary as an input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before training:\n",
      "-ReconstructionError: 1.222305\n",
      "-EnergyCoefficient: 0.129439\n",
      "-HeatCapacity: 0.309532\n",
      "-WeightSparsity: 0.335356\n",
      "-WeightSquare: 1.591978\n",
      "-KLDivergence: 0.169772\n",
      "-ReverseKLDivergence: -0.034053\n",
      "\n",
      "End of epoch 1: \n",
      "Time elapsed 4.801s\n",
      "-ReconstructionError: 0.881006\n",
      "-EnergyCoefficient: 0.260777\n",
      "-HeatCapacity: 0.715890\n",
      "-WeightSparsity: 0.125025\n",
      "-WeightSquare: 15.063619\n",
      "-KLDivergence: 0.112690\n",
      "-ReverseKLDivergence: 0.132180\n",
      "\n",
      "End of epoch 2: \n",
      "Time elapsed 4.841s\n",
      "-ReconstructionError: 0.824033\n",
      "-EnergyCoefficient: 0.348858\n",
      "-HeatCapacity: 0.453395\n",
      "-WeightSparsity: 0.114361\n",
      "-WeightSquare: 26.636614\n",
      "-KLDivergence: 0.104162\n",
      "-ReverseKLDivergence: 0.268652\n",
      "\n",
      "End of epoch 3: \n",
      "Time elapsed 4.894s\n",
      "-ReconstructionError: 0.778112\n",
      "-EnergyCoefficient: 0.262489\n",
      "-HeatCapacity: 1.410929\n",
      "-WeightSparsity: 0.105829\n",
      "-WeightSquare: 37.555742\n",
      "-KLDivergence: 0.107119\n",
      "-ReverseKLDivergence: 0.159505\n",
      "\n",
      "End of epoch 4: \n",
      "Time elapsed 4.898s\n",
      "-ReconstructionError: 0.756907\n",
      "-EnergyCoefficient: 0.389091\n",
      "-HeatCapacity: 1.117362\n",
      "-WeightSparsity: 0.095823\n",
      "-WeightSquare: 48.427056\n",
      "-KLDivergence: 0.134517\n",
      "-ReverseKLDivergence: 0.326323\n",
      "\n",
      "End of epoch 5: \n",
      "Time elapsed 4.907s\n",
      "-ReconstructionError: 0.732729\n",
      "-EnergyCoefficient: 0.304107\n",
      "-HeatCapacity: 0.971900\n",
      "-WeightSparsity: 0.087487\n",
      "-WeightSquare: 58.764663\n",
      "-KLDivergence: 0.085462\n",
      "-ReverseKLDivergence: 0.192505\n",
      "\n",
      "End of epoch 6: \n",
      "Time elapsed 4.896s\n",
      "-ReconstructionError: 0.715532\n",
      "-EnergyCoefficient: 0.254091\n",
      "-HeatCapacity: 1.280490\n",
      "-WeightSparsity: 0.080976\n",
      "-WeightSquare: 70.275249\n",
      "-KLDivergence: 0.073964\n",
      "-ReverseKLDivergence: 0.172438\n",
      "\n",
      "End of epoch 7: \n",
      "Time elapsed 4.853s\n",
      "-ReconstructionError: 0.699906\n",
      "-EnergyCoefficient: 0.239459\n",
      "-HeatCapacity: 1.415814\n",
      "-WeightSparsity: 0.074796\n",
      "-WeightSquare: 80.933345\n",
      "-KLDivergence: 0.063625\n",
      "-ReverseKLDivergence: 0.152264\n",
      "\n",
      "End of epoch 8: \n",
      "Time elapsed 4.867s\n",
      "-ReconstructionError: 0.690501\n",
      "-EnergyCoefficient: 0.312032\n",
      "-HeatCapacity: 0.590963\n",
      "-WeightSparsity: 0.069909\n",
      "-WeightSquare: 92.456055\n",
      "-KLDivergence: 0.075311\n",
      "-ReverseKLDivergence: 0.263548\n",
      "\n",
      "End of epoch 9: \n",
      "Time elapsed 5.151s\n",
      "-ReconstructionError: 0.672954\n",
      "-EnergyCoefficient: 0.278820\n",
      "-HeatCapacity: 1.267690\n",
      "-WeightSparsity: 0.064643\n",
      "-WeightSquare: 102.067402\n",
      "-KLDivergence: 0.044447\n",
      "-ReverseKLDivergence: 0.237113\n",
      "\n",
      "End of epoch 10: \n",
      "Time elapsed 5.94s\n",
      "-ReconstructionError: 0.676011\n",
      "-EnergyCoefficient: 0.313917\n",
      "-HeatCapacity: 1.225270\n",
      "-WeightSparsity: 0.060904\n",
      "-WeightSquare: 113.680352\n",
      "-KLDivergence: 0.084722\n",
      "-ReverseKLDivergence: 0.235839\n",
      "\n",
      "End of epoch 11: \n",
      "Time elapsed 4.88s\n",
      "-ReconstructionError: 0.652318\n",
      "-EnergyCoefficient: 0.236229\n",
      "-HeatCapacity: 1.282272\n",
      "-WeightSparsity: 0.057418\n",
      "-WeightSquare: 124.695684\n",
      "-KLDivergence: 0.069479\n",
      "-ReverseKLDivergence: 0.149445\n",
      "\n",
      "End of epoch 12: \n",
      "Time elapsed 4.85s\n",
      "-ReconstructionError: 0.655321\n",
      "-EnergyCoefficient: 0.251762\n",
      "-HeatCapacity: 2.075053\n",
      "-WeightSparsity: 0.054574\n",
      "-WeightSquare: 133.948350\n",
      "-KLDivergence: 0.054972\n",
      "-ReverseKLDivergence: 0.162227\n",
      "\n",
      "End of epoch 13: \n",
      "Time elapsed 5.005s\n",
      "-ReconstructionError: 0.639309\n",
      "-EnergyCoefficient: 0.255170\n",
      "-HeatCapacity: 1.539652\n",
      "-WeightSparsity: 0.051956\n",
      "-WeightSquare: 142.371250\n",
      "-KLDivergence: 0.067606\n",
      "-ReverseKLDivergence: 0.162965\n",
      "\n",
      "End of epoch 14: \n",
      "Time elapsed 4.958s\n",
      "-ReconstructionError: 0.643696\n",
      "-EnergyCoefficient: 0.291447\n",
      "-HeatCapacity: 1.218738\n",
      "-WeightSparsity: 0.049873\n",
      "-WeightSquare: 150.130039\n",
      "-KLDivergence: 0.091319\n",
      "-ReverseKLDivergence: 0.222105\n",
      "\n",
      "End of epoch 15: \n",
      "Time elapsed 9.33s\n",
      "-ReconstructionError: 0.626424\n",
      "-EnergyCoefficient: 0.251856\n",
      "-HeatCapacity: 1.214857\n",
      "-WeightSparsity: 0.048262\n",
      "-WeightSquare: 160.315273\n",
      "-KLDivergence: 0.042872\n",
      "-ReverseKLDivergence: 0.200629\n",
      "\n",
      "End of epoch 16: \n",
      "Time elapsed 5.185s\n",
      "-ReconstructionError: 0.630208\n",
      "-EnergyCoefficient: 0.309211\n",
      "-HeatCapacity: 2.277996\n",
      "-WeightSparsity: 0.046390\n",
      "-WeightSquare: 166.880566\n",
      "-KLDivergence: 0.064089\n",
      "-ReverseKLDivergence: 0.240856\n",
      "\n",
      "End of epoch 17: \n",
      "Time elapsed 5.133s\n",
      "-ReconstructionError: 0.624927\n",
      "-EnergyCoefficient: 0.252577\n",
      "-HeatCapacity: 2.374191\n",
      "-WeightSparsity: 0.045269\n",
      "-WeightSquare: 175.233457\n",
      "-KLDivergence: 0.033771\n",
      "-ReverseKLDivergence: 0.179779\n",
      "\n",
      "End of epoch 18: \n",
      "Time elapsed 5.207s\n",
      "-ReconstructionError: 0.615037\n",
      "-EnergyCoefficient: 0.231270\n",
      "-HeatCapacity: 1.677584\n",
      "-WeightSparsity: 0.044066\n",
      "-WeightSquare: 182.442188\n",
      "-KLDivergence: 0.059732\n",
      "-ReverseKLDivergence: 0.151763\n",
      "\n",
      "End of epoch 19: \n",
      "Time elapsed 5.455s\n",
      "-ReconstructionError: 0.616561\n",
      "-EnergyCoefficient: 0.326176\n",
      "-HeatCapacity: 3.047941\n",
      "-WeightSparsity: 0.042922\n",
      "-WeightSquare: 190.627500\n",
      "-KLDivergence: 0.068351\n",
      "-ReverseKLDivergence: 0.281011\n",
      "\n",
      "End of epoch 20: \n",
      "Time elapsed 4.984s\n",
      "-ReconstructionError: 0.611289\n",
      "-EnergyCoefficient: 0.223449\n",
      "-HeatCapacity: 1.539112\n",
      "-WeightSparsity: 0.042138\n",
      "-WeightSquare: 196.834883\n",
      "-KLDivergence: 0.064801\n",
      "-ReverseKLDivergence: 0.122577\n",
      "\n"
     ]
    }
   ],
   "source": [
    "##### Bernoulli RBM with L1 regularizer\n",
    "vis_layer = BernoulliLayer(data.ncols)\n",
    "hid_layer = BernoulliLayer(num_hidden_units)\n",
    "rbm_L1 = BoltzmannMachine([vis_layer, hid_layer])\n",
    "\n",
    "rbm_L1.connections[0].weights.add_penalty({'matrix': pen.l1_penalty(1e-3)})\n",
    "\n",
    "# train Bernoulli RBM with L1 regularizer\n",
    "train_model(rbm_L1,num_epochs,monte_carlo_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To define a deep Boltzmann machine (DBM), we just add more layers, and an L1 penalty for every layer.\n",
    "\n",
    "Recalling the essential trick with layer-wise pre-training to prepare the weights of the DBM, we define a `pretrainer` as an object of the `LayerwisePretrain` class (see code snippet below). This results in a slight modification of the function `train_model`, which we call `train_deep_model`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "training model 0\n",
      "\n",
      "Before training:\n",
      "-ReconstructionError: 1.221663\n",
      "-EnergyCoefficient: 0.130296\n",
      "-HeatCapacity: 0.306654\n",
      "-WeightSparsity: 0.334528\n",
      "-WeightSquare: 1.594905\n",
      "-KLDivergence: 0.170464\n",
      "-ReverseKLDivergence: -0.031645\n",
      "\n",
      "End of epoch 1: \n",
      "Time elapsed 4.64s\n",
      "-ReconstructionError: 0.897787\n",
      "-EnergyCoefficient: 0.330039\n",
      "-HeatCapacity: 1.900314\n",
      "-WeightSparsity: 0.121285\n",
      "-WeightSquare: 16.075042\n",
      "-KLDivergence: 0.115897\n",
      "-ReverseKLDivergence: 0.194866\n",
      "\n",
      "End of epoch 2: \n",
      "Time elapsed 4.743s\n",
      "-ReconstructionError: 0.834230\n",
      "-EnergyCoefficient: 0.300143\n",
      "-HeatCapacity: 1.128196\n",
      "-WeightSparsity: 0.108359\n",
      "-WeightSquare: 27.199172\n",
      "-KLDivergence: 0.105726\n",
      "-ReverseKLDivergence: 0.237437\n",
      "\n",
      "End of epoch 3: \n",
      "Time elapsed 4.811s\n",
      "-ReconstructionError: 0.792339\n",
      "-EnergyCoefficient: 0.333817\n",
      "-HeatCapacity: 1.028570\n",
      "-WeightSparsity: 0.098341\n",
      "-WeightSquare: 37.621743\n",
      "-KLDivergence: 0.084027\n",
      "-ReverseKLDivergence: 0.294918\n",
      "\n",
      "End of epoch 4: \n",
      "Time elapsed 4.576s\n",
      "-ReconstructionError: 0.766486\n",
      "-EnergyCoefficient: 0.367534\n",
      "-HeatCapacity: 0.534739\n",
      "-WeightSparsity: 0.089093\n",
      "-WeightSquare: 49.615903\n",
      "-KLDivergence: 0.079035\n",
      "-ReverseKLDivergence: 0.342840\n",
      "\n",
      "End of epoch 5: \n",
      "Time elapsed 4.619s\n",
      "-ReconstructionError: 0.735199\n",
      "-EnergyCoefficient: 0.291658\n",
      "-HeatCapacity: 0.804608\n",
      "-WeightSparsity: 0.081391\n",
      "-WeightSquare: 61.619092\n",
      "-KLDivergence: 0.080433\n",
      "-ReverseKLDivergence: 0.210181\n",
      "\n",
      "End of epoch 6: \n",
      "Time elapsed 5.493s\n",
      "-ReconstructionError: 0.714818\n",
      "-EnergyCoefficient: 0.300214\n",
      "-HeatCapacity: 1.132068\n",
      "-WeightSparsity: 0.075121\n",
      "-WeightSquare: 73.283652\n",
      "-KLDivergence: 0.087811\n",
      "-ReverseKLDivergence: 0.234556\n",
      "\n",
      "End of epoch 7: \n",
      "Time elapsed 5.426s\n",
      "-ReconstructionError: 0.697325\n",
      "-EnergyCoefficient: 0.309640\n",
      "-HeatCapacity: 2.115188\n",
      "-WeightSparsity: 0.069183\n",
      "-WeightSquare: 86.071553\n",
      "-KLDivergence: 0.096619\n",
      "-ReverseKLDivergence: 0.223758\n",
      "\n",
      "End of epoch 8: \n",
      "Time elapsed 5.591s\n",
      "-ReconstructionError: 0.702620\n",
      "-EnergyCoefficient: 0.378565\n",
      "-HeatCapacity: 1.464943\n",
      "-WeightSparsity: 0.064580\n",
      "-WeightSquare: 97.485791\n",
      "-KLDivergence: 0.097712\n",
      "-ReverseKLDivergence: 0.341285\n",
      "\n",
      "End of epoch 9: \n",
      "Time elapsed 5.042s\n",
      "-ReconstructionError: 0.672538\n",
      "-EnergyCoefficient: 0.273587\n",
      "-HeatCapacity: 0.977718\n",
      "-WeightSparsity: 0.061104\n",
      "-WeightSquare: 110.334033\n",
      "-KLDivergence: 0.061797\n",
      "-ReverseKLDivergence: 0.210872\n",
      "\n",
      "End of epoch 10: \n",
      "Time elapsed 4.833s\n",
      "-ReconstructionError: 0.676160\n",
      "-EnergyCoefficient: 0.304087\n",
      "-HeatCapacity: 2.420781\n",
      "-WeightSparsity: 0.057167\n",
      "-WeightSquare: 121.753838\n",
      "-KLDivergence: 0.092384\n",
      "-ReverseKLDivergence: 0.230855\n",
      "\n",
      "End of epoch 11: \n",
      "Time elapsed 4.716s\n",
      "-ReconstructionError: 0.661733\n",
      "-EnergyCoefficient: 0.297026\n",
      "-HeatCapacity: 1.008487\n",
      "-WeightSparsity: 0.054142\n",
      "-WeightSquare: 132.431445\n",
      "-KLDivergence: 0.092672\n",
      "-ReverseKLDivergence: 0.211815\n",
      "\n",
      "End of epoch 12: \n",
      "Time elapsed 4.681s\n",
      "-ReconstructionError: 0.646544\n",
      "-EnergyCoefficient: 0.298972\n",
      "-HeatCapacity: 1.360173\n",
      "-WeightSparsity: 0.051659\n",
      "-WeightSquare: 142.838096\n",
      "-KLDivergence: 0.071754\n",
      "-ReverseKLDivergence: 0.224718\n",
      "\n",
      "End of epoch 13: \n",
      "Time elapsed 4.68s\n",
      "-ReconstructionError: 0.645190\n",
      "-EnergyCoefficient: 0.238612\n",
      "-HeatCapacity: 1.140097\n",
      "-WeightSparsity: 0.048885\n",
      "-WeightSquare: 152.413008\n",
      "-KLDivergence: 0.078194\n",
      "-ReverseKLDivergence: 0.139367\n",
      "\n",
      "End of epoch 14: \n",
      "Time elapsed 4.631s\n",
      "-ReconstructionError: 0.644182\n",
      "-EnergyCoefficient: 0.261230\n",
      "-HeatCapacity: 1.327638\n",
      "-WeightSparsity: 0.047148\n",
      "-WeightSquare: 162.254736\n",
      "-KLDivergence: 0.078020\n",
      "-ReverseKLDivergence: 0.163457\n",
      "\n",
      "End of epoch 15: \n",
      "Time elapsed 4.691s\n",
      "-ReconstructionError: 0.639049\n",
      "-EnergyCoefficient: 0.267432\n",
      "-HeatCapacity: 1.866244\n",
      "-WeightSparsity: 0.045180\n",
      "-WeightSquare: 168.801035\n",
      "-KLDivergence: 0.053338\n",
      "-ReverseKLDivergence: 0.177011\n",
      "\n",
      "End of epoch 16: \n",
      "Time elapsed 5.598s\n",
      "-ReconstructionError: 0.629917\n",
      "-EnergyCoefficient: 0.232822\n",
      "-HeatCapacity: 2.396175\n",
      "-WeightSparsity: 0.043652\n",
      "-WeightSquare: 177.000254\n",
      "-KLDivergence: 0.053509\n",
      "-ReverseKLDivergence: 0.137328\n",
      "\n",
      "End of epoch 17: \n",
      "Time elapsed 4.595s\n",
      "-ReconstructionError: 0.625176\n",
      "-EnergyCoefficient: 0.254991\n",
      "-HeatCapacity: 1.896801\n",
      "-WeightSparsity: 0.043087\n",
      "-WeightSquare: 185.302871\n",
      "-KLDivergence: 0.041568\n",
      "-ReverseKLDivergence: 0.168293\n",
      "\n",
      "End of epoch 18: \n",
      "Time elapsed 4.537s\n",
      "-ReconstructionError: 0.618714\n",
      "-EnergyCoefficient: 0.283417\n",
      "-HeatCapacity: 2.175490\n",
      "-WeightSparsity: 0.041696\n",
      "-WeightSquare: 193.620371\n",
      "-KLDivergence: 0.071575\n",
      "-ReverseKLDivergence: 0.192665\n",
      "\n",
      "End of epoch 19: \n",
      "Time elapsed 4.82s\n",
      "-ReconstructionError: 0.618834\n",
      "-EnergyCoefficient: 0.306351\n",
      "-HeatCapacity: 1.367643\n",
      "-WeightSparsity: 0.040947\n",
      "-WeightSquare: 201.224727\n",
      "-KLDivergence: 0.098637\n",
      "-ReverseKLDivergence: 0.232264\n",
      "\n",
      "End of epoch 20: \n",
      "Time elapsed 4.912s\n",
      "-ReconstructionError: 0.615922\n",
      "-EnergyCoefficient: 0.262865\n",
      "-HeatCapacity: 2.246003\n",
      "-WeightSparsity: 0.040175\n",
      "-WeightSquare: 207.276465\n",
      "-KLDivergence: 0.049488\n",
      "-ReverseKLDivergence: 0.168674\n",
      "\n",
      "training model 1\n",
      "\n",
      "Before training:\n",
      "-ReconstructionError: 1.817938\n",
      "-EnergyCoefficient: 0.625048\n",
      "-HeatCapacity: 0.420704\n",
      "-WeightSparsity: 0.341994\n",
      "-WeightSquare: 1.009060\n",
      "-KLDivergence: 0.596374\n",
      "-ReverseKLDivergence: 0.546756\n",
      "\n",
      "End of epoch 1: \n",
      "Time elapsed 3.181s\n",
      "-ReconstructionError: 0.955236\n",
      "-EnergyCoefficient: 0.329619\n",
      "-HeatCapacity: 30.613847\n",
      "-WeightSparsity: 0.184892\n",
      "-WeightSquare: 2.666410\n",
      "-KLDivergence: 0.134106\n",
      "-ReverseKLDivergence: 0.131400\n",
      "\n",
      "End of epoch 2: \n",
      "Time elapsed 3.189s\n",
      "-ReconstructionError: 0.896282\n",
      "-EnergyCoefficient: 0.329200\n",
      "-HeatCapacity: 10.823931\n",
      "-WeightSparsity: 0.187817\n",
      "-WeightSquare: 3.637917\n",
      "-KLDivergence: 0.206394\n",
      "-ReverseKLDivergence: 0.077495\n",
      "\n",
      "End of epoch 3: \n",
      "Time elapsed 3.185s\n",
      "-ReconstructionError: 0.857668\n",
      "-EnergyCoefficient: 0.391934\n",
      "-HeatCapacity: 16.407195\n",
      "-WeightSparsity: 0.189958\n",
      "-WeightSquare: 4.606170\n",
      "-KLDivergence: 0.231607\n",
      "-ReverseKLDivergence: 0.125489\n",
      "\n",
      "End of epoch 4: \n",
      "Time elapsed 3.193s\n",
      "-ReconstructionError: 0.831441\n",
      "-EnergyCoefficient: 0.381796\n",
      "-HeatCapacity: 20.263775\n",
      "-WeightSparsity: 0.185372\n",
      "-WeightSquare: 5.616452\n",
      "-KLDivergence: 0.222887\n",
      "-ReverseKLDivergence: 0.116399\n",
      "\n",
      "End of epoch 5: \n",
      "Time elapsed 3.184s\n",
      "-ReconstructionError: 0.807041\n",
      "-EnergyCoefficient: 0.345295\n",
      "-HeatCapacity: 13.585340\n",
      "-WeightSparsity: 0.179775\n",
      "-WeightSquare: 6.814833\n",
      "-KLDivergence: 0.213225\n",
      "-ReverseKLDivergence: 0.129081\n",
      "\n",
      "End of epoch 6: \n",
      "Time elapsed 3.176s\n",
      "-ReconstructionError: 0.801588\n",
      "-EnergyCoefficient: 0.402666\n",
      "-HeatCapacity: 3.839240\n",
      "-WeightSparsity: 0.172821\n",
      "-WeightSquare: 7.918809\n",
      "-KLDivergence: 0.289987\n",
      "-ReverseKLDivergence: 0.104544\n",
      "\n",
      "End of epoch 7: \n",
      "Time elapsed 3.182s\n",
      "-ReconstructionError: 0.798056\n",
      "-EnergyCoefficient: 0.447261\n",
      "-HeatCapacity: 2.769902\n",
      "-WeightSparsity: 0.165890\n",
      "-WeightSquare: 9.047374\n",
      "-KLDivergence: 0.329895\n",
      "-ReverseKLDivergence: 0.174177\n",
      "\n",
      "End of epoch 8: \n",
      "Time elapsed 3.182s\n",
      "-ReconstructionError: 0.770556\n",
      "-EnergyCoefficient: 0.410002\n",
      "-HeatCapacity: 11.281398\n",
      "-WeightSparsity: 0.159723\n",
      "-WeightSquare: 10.403275\n",
      "-KLDivergence: 0.261677\n",
      "-ReverseKLDivergence: 0.181337\n",
      "\n",
      "End of epoch 9: \n",
      "Time elapsed 3.175s\n",
      "-ReconstructionError: 0.772474\n",
      "-EnergyCoefficient: 0.455363\n",
      "-HeatCapacity: 1.785892\n",
      "-WeightSparsity: 0.151335\n",
      "-WeightSquare: 11.752716\n",
      "-KLDivergence: 0.307776\n",
      "-ReverseKLDivergence: 0.199194\n",
      "\n",
      "End of epoch 10: \n",
      "Time elapsed 3.177s\n",
      "-ReconstructionError: 0.754196\n",
      "-EnergyCoefficient: 0.428464\n",
      "-HeatCapacity: 2.313815\n",
      "-WeightSparsity: 0.142717\n",
      "-WeightSquare: 12.806985\n",
      "-KLDivergence: 0.287135\n",
      "-ReverseKLDivergence: 0.170842\n",
      "\n",
      "End of epoch 11: \n",
      "Time elapsed 3.429s\n",
      "-ReconstructionError: 0.740625\n",
      "-EnergyCoefficient: 0.467776\n",
      "-HeatCapacity: 1.957995\n",
      "-WeightSparsity: 0.133774\n",
      "-WeightSquare: 13.728407\n",
      "-KLDivergence: 0.312896\n",
      "-ReverseKLDivergence: 0.221361\n",
      "\n",
      "End of epoch 12: \n",
      "Time elapsed 3.769s\n",
      "-ReconstructionError: 0.725275\n",
      "-EnergyCoefficient: 0.374433\n",
      "-HeatCapacity: 4.990034\n",
      "-WeightSparsity: 0.128008\n",
      "-WeightSquare: 15.451649\n",
      "-KLDivergence: 0.257165\n",
      "-ReverseKLDivergence: 0.150764\n",
      "\n",
      "End of epoch 13: \n",
      "Time elapsed 3.405s\n",
      "-ReconstructionError: 0.733516\n",
      "-EnergyCoefficient: 0.498661\n",
      "-HeatCapacity: 1.503117\n",
      "-WeightSparsity: 0.121149\n",
      "-WeightSquare: 16.865161\n",
      "-KLDivergence: 0.331327\n",
      "-ReverseKLDivergence: 0.319607\n",
      "\n",
      "End of epoch 14: \n",
      "Time elapsed 3.767s\n",
      "-ReconstructionError: 0.711324\n",
      "-EnergyCoefficient: 0.475016\n",
      "-HeatCapacity: 1.945628\n",
      "-WeightSparsity: 0.114787\n",
      "-WeightSquare: 18.455599\n",
      "-KLDivergence: 0.317272\n",
      "-ReverseKLDivergence: 0.266205\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "End of epoch 15: \n",
      "Time elapsed 3.882s\n",
      "-ReconstructionError: 0.719401\n",
      "-EnergyCoefficient: 0.381655\n",
      "-HeatCapacity: 3.408595\n",
      "-WeightSparsity: 0.108113\n",
      "-WeightSquare: 19.306226\n",
      "-KLDivergence: 0.274513\n",
      "-ReverseKLDivergence: 0.131405\n",
      "\n",
      "End of epoch 16: \n",
      "Time elapsed 4.0s\n",
      "-ReconstructionError: 0.701876\n",
      "-EnergyCoefficient: 0.430493\n",
      "-HeatCapacity: 2.594073\n",
      "-WeightSparsity: 0.102073\n",
      "-WeightSquare: 20.328297\n",
      "-KLDivergence: 0.288566\n",
      "-ReverseKLDivergence: 0.164022\n",
      "\n",
      "End of epoch 17: \n",
      "Time elapsed 3.708s\n",
      "-ReconstructionError: 0.700395\n",
      "-EnergyCoefficient: 0.418578\n",
      "-HeatCapacity: 2.056519\n",
      "-WeightSparsity: 0.098243\n",
      "-WeightSquare: 21.668208\n",
      "-KLDivergence: 0.285168\n",
      "-ReverseKLDivergence: 0.211606\n",
      "\n",
      "End of epoch 18: \n",
      "Time elapsed 3.554s\n",
      "-ReconstructionError: 0.690120\n",
      "-EnergyCoefficient: 0.408061\n",
      "-HeatCapacity: 1.474181\n",
      "-WeightSparsity: 0.094199\n",
      "-WeightSquare: 22.563384\n",
      "-KLDivergence: 0.283892\n",
      "-ReverseKLDivergence: 0.190362\n",
      "\n",
      "End of epoch 19: \n",
      "Time elapsed 3.341s\n",
      "-ReconstructionError: 0.681361\n",
      "-EnergyCoefficient: 0.384341\n",
      "-HeatCapacity: 2.581074\n",
      "-WeightSparsity: 0.092489\n",
      "-WeightSquare: 23.452239\n",
      "-KLDivergence: 0.238908\n",
      "-ReverseKLDivergence: 0.208922\n",
      "\n",
      "End of epoch 20: \n",
      "Time elapsed 3.443s\n",
      "-ReconstructionError: 0.687715\n",
      "-EnergyCoefficient: 0.382431\n",
      "-HeatCapacity: 2.516824\n",
      "-WeightSparsity: 0.089389\n",
      "-WeightSquare: 23.989824\n",
      "-KLDivergence: 0.264690\n",
      "-ReverseKLDivergence: 0.181684\n",
      "\n",
      "Before training:\n",
      "-ReconstructionError: 0.811289\n",
      "-EnergyCoefficient: 0.346004\n",
      "-HeatCapacity: 1.908560\n",
      "-WeightSparsity: 0.040175\n",
      "-WeightSquare: 207.276465\n",
      "-KLDivergence: 0.154770\n",
      "-ReverseKLDivergence: 0.227625\n",
      "\n",
      "End of epoch 1: \n",
      "Time elapsed 6.371s\n",
      "-ReconstructionError: 0.739374\n",
      "-EnergyCoefficient: 0.199532\n",
      "-HeatCapacity: 2.174324\n",
      "-WeightSparsity: 0.039709\n",
      "-WeightSquare: 212.923418\n",
      "-KLDivergence: 0.026613\n",
      "-ReverseKLDivergence: 0.090668\n",
      "\n",
      "End of epoch 2: \n",
      "Time elapsed 6.382s\n",
      "-ReconstructionError: 0.732260\n",
      "-EnergyCoefficient: 0.198894\n",
      "-HeatCapacity: 2.910776\n",
      "-WeightSparsity: 0.039151\n",
      "-WeightSquare: 214.452422\n",
      "-KLDivergence: 0.007490\n",
      "-ReverseKLDivergence: 0.101709\n",
      "\n",
      "End of epoch 3: \n",
      "Time elapsed 6.244s\n",
      "-ReconstructionError: 0.735783\n",
      "-EnergyCoefficient: 0.208160\n",
      "-HeatCapacity: 2.305223\n",
      "-WeightSparsity: 0.038712\n",
      "-WeightSquare: 215.891387\n",
      "-KLDivergence: 0.022056\n",
      "-ReverseKLDivergence: 0.098389\n",
      "\n",
      "End of epoch 4: \n",
      "Time elapsed 6.512s\n",
      "-ReconstructionError: 0.734180\n",
      "-EnergyCoefficient: 0.194220\n",
      "-HeatCapacity: 1.986777\n",
      "-WeightSparsity: 0.038115\n",
      "-WeightSquare: 216.731367\n",
      "-KLDivergence: 0.024976\n",
      "-ReverseKLDivergence: 0.087987\n",
      "\n",
      "End of epoch 5: \n",
      "Time elapsed 6.381s\n",
      "-ReconstructionError: 0.736551\n",
      "-EnergyCoefficient: 0.206767\n",
      "-HeatCapacity: 1.662948\n",
      "-WeightSparsity: 0.037563\n",
      "-WeightSquare: 217.601973\n",
      "-KLDivergence: 0.037015\n",
      "-ReverseKLDivergence: 0.104847\n",
      "\n",
      "End of epoch 6: \n",
      "Time elapsed 6.171s\n",
      "-ReconstructionError: 0.732770\n",
      "-EnergyCoefficient: 0.213407\n",
      "-HeatCapacity: 1.695885\n",
      "-WeightSparsity: 0.036975\n",
      "-WeightSquare: 218.225234\n",
      "-KLDivergence: 0.025131\n",
      "-ReverseKLDivergence: 0.103925\n",
      "\n",
      "End of epoch 7: \n",
      "Time elapsed 6.411s\n",
      "-ReconstructionError: 0.730597\n",
      "-EnergyCoefficient: 0.228237\n",
      "-HeatCapacity: 1.512862\n",
      "-WeightSparsity: 0.036375\n",
      "-WeightSquare: 218.699844\n",
      "-KLDivergence: 0.031608\n",
      "-ReverseKLDivergence: 0.121394\n",
      "\n",
      "End of epoch 8: \n",
      "Time elapsed 6.283s\n",
      "-ReconstructionError: 0.727227\n",
      "-EnergyCoefficient: 0.181289\n",
      "-HeatCapacity: 1.818269\n",
      "-WeightSparsity: 0.035773\n",
      "-WeightSquare: 218.985273\n",
      "-KLDivergence: 0.022548\n",
      "-ReverseKLDivergence: 0.085181\n",
      "\n",
      "End of epoch 9: \n",
      "Time elapsed 6.28s\n",
      "-ReconstructionError: 0.720785\n",
      "-EnergyCoefficient: 0.240146\n",
      "-HeatCapacity: 1.582654\n",
      "-WeightSparsity: 0.035257\n",
      "-WeightSquare: 219.680371\n",
      "-KLDivergence: 0.034347\n",
      "-ReverseKLDivergence: 0.127287\n",
      "\n",
      "End of epoch 10: \n",
      "Time elapsed 5.999s\n",
      "-ReconstructionError: 0.718667\n",
      "-EnergyCoefficient: 0.196960\n",
      "-HeatCapacity: 1.710515\n",
      "-WeightSparsity: 0.034692\n",
      "-WeightSquare: 220.185234\n",
      "-KLDivergence: 0.030763\n",
      "-ReverseKLDivergence: 0.095320\n",
      "\n",
      "End of epoch 11: \n",
      "Time elapsed 6.409s\n",
      "-ReconstructionError: 0.712717\n",
      "-EnergyCoefficient: 0.232311\n",
      "-HeatCapacity: 1.657680\n",
      "-WeightSparsity: 0.034277\n",
      "-WeightSquare: 221.409512\n",
      "-KLDivergence: 0.030061\n",
      "-ReverseKLDivergence: 0.127994\n",
      "\n",
      "End of epoch 12: \n",
      "Time elapsed 6.392s\n",
      "-ReconstructionError: 0.711360\n",
      "-EnergyCoefficient: 0.181281\n",
      "-HeatCapacity: 1.901625\n",
      "-WeightSparsity: 0.033741\n",
      "-WeightSquare: 222.095410\n",
      "-KLDivergence: 0.024610\n",
      "-ReverseKLDivergence: 0.081649\n",
      "\n",
      "End of epoch 13: \n",
      "Time elapsed 6.023s\n",
      "-ReconstructionError: 0.705936\n",
      "-EnergyCoefficient: 0.197606\n",
      "-HeatCapacity: 1.615389\n",
      "-WeightSparsity: 0.033234\n",
      "-WeightSquare: 222.602168\n",
      "-KLDivergence: 0.027221\n",
      "-ReverseKLDivergence: 0.095061\n",
      "\n",
      "End of epoch 14: \n",
      "Time elapsed 6.295s\n",
      "-ReconstructionError: 0.704527\n",
      "-EnergyCoefficient: 0.202553\n",
      "-HeatCapacity: 1.693487\n",
      "-WeightSparsity: 0.032778\n",
      "-WeightSquare: 223.237363\n",
      "-KLDivergence: 0.023307\n",
      "-ReverseKLDivergence: 0.105222\n",
      "\n",
      "End of epoch 15: \n",
      "Time elapsed 6.753s\n",
      "-ReconstructionError: 0.699067\n",
      "-EnergyCoefficient: 0.197803\n",
      "-HeatCapacity: 1.532241\n",
      "-WeightSparsity: 0.032433\n",
      "-WeightSquare: 224.556113\n",
      "-KLDivergence: 0.027205\n",
      "-ReverseKLDivergence: 0.087578\n",
      "\n",
      "End of epoch 16: \n",
      "Time elapsed 6.192s\n",
      "-ReconstructionError: 0.693411\n",
      "-EnergyCoefficient: 0.199328\n",
      "-HeatCapacity: 2.456449\n",
      "-WeightSparsity: 0.032126\n",
      "-WeightSquare: 225.941543\n",
      "-KLDivergence: 0.009409\n",
      "-ReverseKLDivergence: 0.101786\n",
      "\n",
      "End of epoch 17: \n",
      "Time elapsed 6.461s\n",
      "-ReconstructionError: 0.689332\n",
      "-EnergyCoefficient: 0.200686\n",
      "-HeatCapacity: 1.691124\n",
      "-WeightSparsity: 0.031796\n",
      "-WeightSquare: 227.097637\n",
      "-KLDivergence: 0.024309\n",
      "-ReverseKLDivergence: 0.104585\n",
      "\n",
      "End of epoch 18: \n",
      "Time elapsed 6.012s\n",
      "-ReconstructionError: 0.685113\n",
      "-EnergyCoefficient: 0.201751\n",
      "-HeatCapacity: 1.666984\n",
      "-WeightSparsity: 0.031540\n",
      "-WeightSquare: 228.750156\n",
      "-KLDivergence: 0.020524\n",
      "-ReverseKLDivergence: 0.106222\n",
      "\n",
      "End of epoch 19: \n",
      "Time elapsed 6.251s\n",
      "-ReconstructionError: 0.684345\n",
      "-EnergyCoefficient: 0.197851\n",
      "-HeatCapacity: 1.700418\n",
      "-WeightSparsity: 0.031248\n",
      "-WeightSquare: 230.065430\n",
      "-KLDivergence: 0.024734\n",
      "-ReverseKLDivergence: 0.099089\n",
      "\n",
      "End of epoch 20: \n",
      "Time elapsed 6.393s\n",
      "-ReconstructionError: 0.683919\n",
      "-EnergyCoefficient: 0.233017\n",
      "-HeatCapacity: 1.528317\n",
      "-WeightSparsity: 0.030920\n",
      "-WeightSquare: 231.103750\n",
      "-KLDivergence: 0.024362\n",
      "-ReverseKLDivergence: 0.142374\n",
      "\n"
     ]
    }
   ],
   "source": [
    "##### Deep Boltzmann Machine\n",
    "# set up the model\n",
    "dbm = BoltzmannMachine([BernoulliLayer(data.ncols), # visible layer\n",
    "                        BernoulliLayer(num_hidden_units), # hidden layer 1\n",
    "                        BernoulliLayer(num_hidden_units) # hidden layer 2\n",
    "                       ])\n",
    "\n",
    "# add an L1 penalty to the weights\n",
    "for conn in dbm.connections:\n",
    "    conn.weights.add_penalty({'matrix':pen.l1_penalty(1e-3)})\n",
    "    \n",
    "# add pre-training \t\n",
    "def train_deep_model(model,num_epochs,monte_carlo_steps):\n",
    "    # make a simple guess for the initial parameters of the model\n",
    "    model.initialize(data,method='glorot_normal')\n",
    "    # set SGD rπetrain optimizer\n",
    "    opt=ADAM_optimizer(1E-2,1.0)\n",
    "    # pre-train model\n",
    "    pretrainer=fit.LayerwisePretrain(model,data)\n",
    "    pretrainer.train(opt, num_epochs, method=fit.pcd, mcsteps=monte_carlo_steps, init_method=\"glorot_normal\")\n",
    "    # set SGD train optimizer\n",
    "    opt=ADAM_optimizer(1E-3,1.0)\n",
    "    # train model\n",
    "    trainer=fit.SGD(model,data)\n",
    "    trainer.train(opt,num_epochs,method=fit.pcd,mcsteps=monte_carlo_steps)\n",
    "# train DBM\n",
    "train_deep_model(dbm,num_epochs,monte_carlo_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the MNIST Dataset\n",
    "\n",
    "Let us look at a couple of random examples to get an idea how the data we are dealing with actually looks like.\n",
    "\n",
    "To do this, we define the function  `plot_image_grid()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABHQAAACECAYAAADx0Xy8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCCPQAQAAAAjzG1+hpEzKfRjhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11057e5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.gridspec as gs\n",
    "import matplotlib.cm as cm\n",
    "import seaborn as sns\n",
    "\n",
    "# make sure the plots are shown in the notebook\n",
    "\n",
    "def plot_image_grid(image_array, shape, vmin=0, vmax=1, cmap=cm.gray_r, row_titles=None):\n",
    "    array = be.to_numpy_array(image_array)\n",
    "    nrows, ncols = array.shape[:-1]\n",
    "    f = plt.figure(figsize=(2*ncols, 2*nrows))\n",
    "    grid = gs.GridSpec(nrows, ncols)\n",
    "    axes = [[plt.subplot(grid[i,j]) for j in range(ncols)] for i in range(nrows)]\n",
    "    for i in range(nrows):\n",
    "        for j in range(ncols):\n",
    "            sns.heatmap(np.reshape(array[i][j], shape),\n",
    "                ax=axes[i][j], cmap=cmap, cbar=False, vmin=vmin, vmax=vmax)\n",
    "            axes[i][j].set(yticks=[])\n",
    "            axes[i][j].set(xticks=[])\n",
    "\n",
    "    if row_titles is not None:\n",
    "        for i in range(nrows):\n",
    "            axes[i][0].set_ylabel(row_titles[i], fontsize=36)\n",
    "            \n",
    "    plt.tight_layout()\n",
    "    plt.show(f)\n",
    "    plt.close(f)\n",
    "    \n",
    "\n",
    "image_shape = (28, 28) # 28x28 = 784 pixels in every image\n",
    "num_to_plot = 8 # of data points to plot\n",
    "\n",
    "examples = data.get(mode='train') # shape (batch_size, 784)\n",
    "\n",
    "example_plot = plot_image_grid(np.expand_dims(examples[:num_to_plot], 0), \n",
    "                               image_shape, vmin=0, vmax=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reconstructions\n",
    "\n",
    "Having trained our models, let us see how they perform by computing some reconstructions from the validation data. \n",
    "\n",
    "Recall that a reconstruction ${\\bf v'}$ of a given data point ${\\bf x}$ is computed in two steps: (i) we fix the visible layer ${\\bf v}={\\bf x}$ to be the data, and use MC sampling to find the state of the hidden layer ${\\bf h}$ which maximizes the probability distribution $p({\\bf h}\\vert{\\bf v})$, (ii) fixing the same obtained state ${\\bf h}$, we find the reconstruction of the visible layer ${\\bf v'}$ which maximizes the probability $p({\\bf v'}\\vert{\\bf h})$. In the case of a DBM, the forward pass continues until we reach the last of the hidden layers, and the backward pass goes in reverse. \n",
    "\n",
    "To compute reconstructions, we define a MC `sampler` based on the trained `model`. The stating point form the MC sampler is set using the `set_state()` method. To compute reconstructions, we need to keep the probability distribution encoded in the `model` fixed which is done with the help of the `deterministic_iteration` function method, which takes the number of weights `num_weights` in the model, and the state of the sampler `sampler.state` as required arguments. We can combine these steps in the function `compute_reconstructions`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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A0LQqmnK1bdu2uPHGG2PGjBmxYsWK9n/vbFcdh0qNHz8+LrzwwjjjjDMqKC7VMuWqvAxF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\n0Y9y2y4AAABAnaUKdLZv3x5JksTFF18cY8eOzW3nZ599dlx00UXRaDR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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1105a0b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##### compute reconstructions\n",
    "def compute_reconstructions(model, data):\n",
    "    \"\"\"\n",
    "    Computes reconstructions of the input data.\n",
    "    Input v -> h -> v' (one pass up one pass down)\n",
    "    \n",
    "    Args:\n",
    "        model: a model\n",
    "        data: a tensor of shape (num_samples, num_visible_units)\n",
    "\n",
    "    Returns:\n",
    "        tensor of shape (num_samples, num_visible_units)\n",
    "    \n",
    "    \"\"\"\n",
    "    recons = model.compute_reconstructions(data).get_visible()\n",
    "    return be.to_numpy_array(recons)\n",
    "\n",
    "examples = data.get(mode='validate') # shape (batch_size, 784)\n",
    "data.reset_generator(mode='validate') # reset the generator to the beginning of the validation set\n",
    "\n",
    "hopfield_reconstructions = compute_reconstructions(hopfield, examples[:num_to_plot])\n",
    "rbm_reconstructions = compute_reconstructions(rbm, examples[:num_to_plot])\n",
    "rbm_L1_reconstructions = compute_reconstructions(rbm_L1, examples[:num_to_plot])\n",
    "dbm_reconstructions = compute_reconstructions(dbm, examples[:num_to_plot])\n",
    "\n",
    "reconstruction_plot = plot_image_grid(\n",
    "    np.array([examples[:num_to_plot], \n",
    "                 hopfield_reconstructions, \n",
    "                 rbm_reconstructions, \n",
    "                 rbm_L1_reconstructions,\n",
    "                 dbm_reconstructions]), \n",
    "    image_shape, vmin=0, vmax=1, row_titles=[\"Data\", \"Hopfield\", \"RBM\", \"RBM (L1)\", \"DBM\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fantasy Particles\n",
    "\n",
    "Once we have the trained models ready, we can use MC to draw samples from the corresponding probability distributions, called \"fantasy particles\". To this end let us draw a `random_sample` from the validation data, and compute the `model_state`. Next, we define a MC `sampler` based on the `model`, and set its state to `model_state`. To compute the fantasy particles, we do layer-wise Gibbs sampling for a total of `n_steps` equilibration steps. The last step (controlled by the boolean `mean_field`) is a final mean-field iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3blxexWAfRf8wtSqBDtVwQ0QjaX+tp0hf3rWjYihSm4jQLsrC9aP1FP07qEAn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\nAACgYP4PYO0p/GVI2kwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12898aa20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def compute_fantasy_particles(model,num_fantasy,num_steps,mean_field=True):\n",
    "    \"\"\"\n",
    "    Draws samples from the model using Gibbs sampling Markov Chain Monte Carlo .\n",
    "    Starts from randomly initialized points. \n",
    "\n",
    "    Args:\n",
    "        model: a model\n",
    "        data: a tensor of shape (num_samples, num_visible_units)\n",
    "        num_steps (int): the number of update steps\n",
    "        mean_field (bool; optional): run a final mean field step to compute probabilities\n",
    "\n",
    "    Returns:\n",
    "        tensor of shape (num_samples, num_visible_units)\n",
    "    \n",
    "    \"\"\"\n",
    "    schedule = schedules.Linear(initial=1.0, delta = 1 / (num_steps-1))\n",
    "    fantasy = samplers.SequentialMC.generate_fantasy_state(model,\n",
    "                                                           num_fantasy,\n",
    "                                                           num_steps,\n",
    "                                                           schedule=schedule,\n",
    "                                                           beta_std=0.0,\n",
    "                                                           beta_momentum=0.0)\n",
    "    if mean_field:\n",
    "        fantasy = model.mean_field_iteration(1, fantasy)\n",
    "    fantasy_particles = fantasy.get_visible()        \n",
    "    return be.to_numpy_array(fantasy_particles)\n",
    "\n",
    "examples = data.get(mode='validate') # shape (batch_size, 784)\n",
    "data.reset_generator(mode='validate') # reset the generator to the beginning of the validation set\n",
    "\n",
    "hopfield_fantasy = compute_fantasy_particles(hopfield, num_to_plot, 100, mean_field=False)\n",
    "rbm_fantasy = compute_fantasy_particles(rbm, num_to_plot, 100, mean_field=False)\n",
    "rbm_L1_fantasy = compute_fantasy_particles(rbm_L1, num_to_plot, 100, mean_field=False)\n",
    "dbm_fantasy = compute_fantasy_particles(dbm, num_to_plot, 100, mean_field=False)\n",
    "\n",
    "fantasy_plot = plot_image_grid(\n",
    "    np.array([hopfield_fantasy, \n",
    "                 rbm_fantasy, \n",
    "                 rbm_L1_fantasy,\n",
    "                 dbm_fantasy]), \n",
    "    image_shape, vmin=0, vmax=1, row_titles=[\"Hopfield\", \"RBM\", \"RBM (L1)\", \"DBM\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### De-noising Images\n",
    "\n",
    "One can use generative models to reduce the noise in images (de-noising). Let us randomly flip a fraction, `fraction_to_flip`, of the black & white bits in the validation data, and use the models defined above to reconstruct (de-noise) the digit images:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2bdvi3nvvjQULFsSiRYui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      "text/plain": [
       "<matplotlib.figure.Figure at 0x128975e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##### denoise MNIST images\n",
    "# get validation data\n",
    "examples = data.get(mode='validate') # shape (batch_size, 784)\n",
    "# reset data generator to beginning of the validation set\n",
    "data.reset_generator(mode='validate') \n",
    "\n",
    "# add some noise to the examples by randomly flipping some pixels 0 -> 1 and 1 -> 0\n",
    "fraction_to_flip=0.15\n",
    "# create flipping mask\n",
    "flip_mask=be.rand_like(examples) < fraction_to_flip\n",
    "# compute noisy data\n",
    "noisy_data=(1-flip_mask) * examples + flip_mask * (1 - examples)\n",
    "\n",
    "# define number of digits to display\n",
    "num_to_display=8\n",
    "# compute de-noised images\n",
    "hopfield_denoised=compute_reconstructions(hopfield,noisy_data[:num_to_display])\n",
    "rbm_denoised=compute_reconstructions(rbm,noisy_data[:num_to_display])\n",
    "rbm_L1_denoised=compute_reconstructions(rbm_L1,noisy_data[:num_to_display])\n",
    "dbm_denoised=compute_reconstructions(dbm,noisy_data[:num_to_display])\n",
    "\n",
    "denoising_plot = plot_image_grid(\n",
    "    np.array([examples[:num_to_plot], \n",
    "                 noisy_data[:num_to_plot], \n",
    "                 hopfield_denoised, \n",
    "                 rbm_denoised, \n",
    "                 rbm_L1_denoised,\n",
    "                 dbm_denoised]), \n",
    "    image_shape, vmin=0, vmax=1, row_titles=[\"Data\", \"Noisy\", \"Hopfield\", \"RBM\", \"RBM (L1)\", \"DBM\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weight Visualization\n",
    "\n",
    "Let us open up the black box of our generative models now. Below, we show the features learned by the weights of the different models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9XSozSmS+3El1OEZSw4wdIH5fJWLAmFS6Upw3rStiIvW+uIY4y/OotQ+fR0ko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\neENsjDHGGGMKjTfExhhjjDGm0Pz/Y/+a01DLWEYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fdcc518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the weights of the hopfield model\n",
    "hopfield_weights = plot_image_grid(\n",
    "    be.reshape(hopfield.connections[0].weights.W(trans=True)[:25], (5,5,784)), \n",
    "    image_shape, \n",
    "    vmin=be.tmin(hopfield.connections[0].weights.W()), \n",
    "    vmax=be.tmax(hopfield.connections[0].weights.W()),\n",
    "    cmap=cm.seismic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H2OS778yTT/9txo29zJjVT5aLiqjPTafGGOvaSB80adQIu17HvN++jVlruV0EUjXjff3M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YPNmHEHpmsfzddGM6u6fiNSe7s6LPeGyEH7xkxr5pB7GxSkm1Eoxa2HxSdiVJcmiXAS6Nqc7t+N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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106bc2ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the weights of the RBM\n",
    "rbm_weights = plot_image_grid(\n",
    "    be.reshape(rbm.connections[0].weights.W(trans=True)[:25], (5,5,784)), \n",
    "    image_shape, \n",
    "    vmin=be.tmin(rbm.connections[0].weights.W()), \n",
    "    vmax=be.tmax(rbm.connections[0].weights.W()),\n",
    "    cmap=cm.seismic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JZJSWWp139liXMUGnVVJd7DZLJhW1TNjreU7O8XslCF1kP0uHPlPK5Uv0uIzJ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\noGtMiAEAANA1JsQAAADo2v8DOQU7CL9SPSEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1289ea080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the weights of the L1 regularized RBM\n",
    "rbmL1_weights = plot_image_grid(\n",
    "    be.reshape(rbm_L1.connections[0].weights.W(trans=True)[:25], (5,5,784)), \n",
    "    image_shape, \n",
    "    vmin=be.tmin(rbm_L1.connections[0].weights.W()), \n",
    "    vmax=be.tmax(rbm_L1.connections[0].weights.W()),\n",
    "    cmap=cm.seismic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0WdXXqPrf/vV6oxhoXEp5+bLebO74KoY4Nn26+261jewiR9Nl9W6pdVGvPtMs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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12928d160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the weights of the first layer of the dbm\n",
    "dbm_weights = plot_image_grid(\n",
    "    be.reshape(dbm.connections[0].weights.W(trans=True)[:25], (5,5,784)), \n",
    "    image_shape, \n",
    "    vmin=be.tmin(dbm.connections[0].weights.W()), \n",
    "    vmax=be.tmax(dbm.connections[0].weights.W()),\n",
    "    cmap=cm.seismic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data.close() # close the HDF5 store with the MNIST dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "* Try increasing/decreasing the number of hidden units and study systematically how the performance of the different models changes.\n",
    "* Look up Paysage's documentation and study the performance for various SGD optimizers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}