{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Notebook 19: Variational Autoencoders with Keras and MNIST" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning Goals\n", "The goals of this notebook is to learn how to code a variational autoencoder in Keras. We will discuss hyperparameters, training, and loss-functions. In addition, we will familiarize ourselves with the Keras sequential GUI as well as how to visualize results and make predictions using a VAE with a small number of latent dimensions.\n", "\n", "## Overview\n", "\n", "This notebook teaches the reader how to build a Variational Autoencoder (VAE) with Keras. The code is a minimally modified, stripped-down version of the code from Lous Tiao in his wonderful [blog post](http://tiao.io/posts/implementing-variational-autoencoders-in-keras-beyond-the-quickstart-tutorial/) which the reader is strongly encouraged to also read.\n", "\n", "Our VAE will have Gaussian Latent variables and a Gaussian Posterior distribution $q_\\phi({\\mathbf z}|{\\mathbf x})$ with a diagonal covariance matrix. \n", "\n", "Recall, that a VAE consists of four essential elements:\n", "\n", "* A latent variable ${\\mathbf z}$ drawn from a distribution $p({\\mathbf z})$ which in our case will be a Gaussian with mean zero and standard\n", "deviation $\\epsilon$.\n", "* A decoder $p(\\mathbf{x}|\\mathbf{z})$ that maps latent variables ${\\mathbf z}$ to visible variables ${\\mathbf x}$. In our case, this is just a Multi-Layer Perceptron (MLP) - a neural network with one hidden layer.\n", "* An encoder $q_\\phi(\\mathbf{z}|\\mathbf{x})$ that maps examples to the latent space. In our case, this map is just a Gaussian with means and variances that depend on the input: $q_\\phi({\\bf z}|{\\bf x})= \\mathcal{N}({\\bf z}, \\boldsymbol{\\mu}({\\bf x}), \\mathrm{diag}(\\boldsymbol{\\sigma}^2({\\bf x})))$\n", "* A cost function consisting of two terms: the reconstruction error and an additional regularization term that minimizes the KL-divergence between the variational and true encoders. Mathematically, the reconstruction error is just the cross-entropy between the samples and their reconstructions. The KL-divergence term can be calculated analytically for this term and can be written as\n", "\n", "$$-D_{KL}(q_\\phi({\\bf z}|{\\bf x})|p({\\bf z}))={1 \\over 2} \\sum_{j=1}^J \\left (1+\\log{\\sigma_j^2({\\bf x})}-\\mu_j^2({\\bf x}) -\\sigma_j^2({\\bf x})\\right).\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importing Data and specifying hyperparameters\n", "\n", "In the next section of code, we import the data and specify hyperparameters. The MNIST data are gray scale ranging in values from 0 to 255 for each pixel. We normalize this range to lie between 0 and 1. \n", "\n", "The hyperparameters we need to specify the architecture and train the VAE are:\n", "\n", "* The dimension of the hidden layers for encoders and decoders (intermediate_dim)\n", "* The dimension of the latent space (latent_dim)\n", "* The standard deviation of latent variables (epsilon_std)\n", "* Optimization hyper-parameters: batch_size, epochs\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Using TensorFlow backend.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "(60000, 28, 28, 1)\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import norm\n", "\n", "from keras import backend as K\n", "\n", "from keras.layers import (Input, InputLayer, Dense, Lambda, Layer, \n", " Add, Multiply)\n", "from keras.models import Model, Sequential\n", "from keras.datasets import mnist\n", "import pandas as pd\n", "\n", "\n", "#Load Data and map gray scale 256 to number between zero and 1\n", "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n", "x_train = np.expand_dims(x_train, axis=-1) / 255.\n", "x_test = np.expand_dims(x_test, axis=-1) / 255.\n", "\n", "print(x_train.shape)\n", "\n", "# Find dimensions of input images\n", "img_rows, img_cols, img_chns = x_train.shape[1:]\n", "\n", "# Specify hyperparameters\n", "original_dim = img_rows * img_cols\n", "intermediate_dim = 256\n", "latent_dim = 2\n", "batch_size = 100\n", "epochs = 3\n", "epsilon_std = 1.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Specifying the loss function\n", "\n", "Here we specify the loss function. The first block of code is just the reconstruction error which is given by the cross-entropy. The second block of code calculates the KL-divergence analytically and adds it to the loss function with the line self.add_loss. It represents the KL-divergence as just another layer in the neural network with the inputs equal to the outputs: the means and variances for the variational encoder (i.e. $\\boldsymbol{\\mu}({\\bf x})$ and $\\boldsymbol{\\sigma}^2({\\bf x})$)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def nll(y_true, y_pred):\n", " \"\"\" Negative log likelihood (Bernoulli). \"\"\"\n", "\n", " # keras.losses.binary_crossentropy gives the mean\n", " # over the last axis. we require the sum\n", " return K.sum(K.binary_crossentropy(y_true, y_pred), axis=-1)\n", "\n", "class KLDivergenceLayer(Layer):\n", "\n", " \"\"\" Identity transform layer that adds KL divergence\n", " to the final model loss.\n", " \"\"\"\n", "\n", " def __init__(self, *args, **kwargs):\n", " self.is_placeholder = True\n", " super(KLDivergenceLayer, self).__init__(*args, **kwargs)\n", "\n", " def call(self, inputs):\n", "\n", " mu, log_var = inputs\n", "\n", " kl_batch = - .5 * K.sum(1 + log_var -\n", " K.square(mu) -\n", " K.exp(log_var), axis=-1)\n", "\n", " self.add_loss(K.mean(kl_batch), inputs=inputs)\n", "\n", " return inputs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Encoder and Decoder\n", "\n", "The following specifies both the encoder and decoder. The encoder is a MLP with three layers that maps ${\\bf x}$ to $\\boldsymbol{\\mu}({\\bf x})$ and $\\boldsymbol{\\sigma}^2({\\bf x})$, followed by the generation of a latent variable using the reparametrization trick (see main text). The decoder is specified as a single sequential Keras layer.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Encoder\n", "\n", "x = Input(shape=(original_dim,))\n", "h = Dense(intermediate_dim, activation='relu')(x)\n", "\n", "z_mu = Dense(latent_dim)(h)\n", "z_log_var = Dense(latent_dim)(h)\n", "\n", "z_mu, z_log_var = KLDivergenceLayer()([z_mu, z_log_var])\n", "\n", "# Reparametrization trick\n", "z_sigma = Lambda(lambda t: K.exp(.5*t))(z_log_var)\n", "\n", "eps = Input(tensor=K.random_normal(shape=(K.shape(x)[0], \n", " latent_dim)))\n", "z_eps = Multiply()([z_sigma, eps])\n", "z = Add()([z_mu, z_eps])\n", "\n", "# This defines the Encoder which takes noise and input and outputs\n", "# the latent variable z\n", "encoder = Model(inputs=[x, eps], outputs=z)\n", "\n", "# Decoder is MLP specified as single Keras Sequential Layer\n", "decoder = Sequential([\n", " Dense(intermediate_dim, input_dim=latent_dim, activation='relu'),\n", " Dense(original_dim, activation='sigmoid')\n", "])\n", "\n", "x_pred = decoder(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Training the model\n", "\n", "We now train the model. Even though the loss function is the negative log likelihood (cross-entropy), recall that the KL-layer adds the analytic form of the loss function as well. We also have to reshape the data to make it a vector, and specify an optimizer." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Train on 60000 samples, validate on 10000 samples\n", "Epoch 1/3\n", "60000/60000 [==============================] - 10s 173us/step - loss: 190.8570 - val_loss: 172.5236\n", "Epoch 2/3\n", "60000/60000 [==============================] - 10s 173us/step - loss: 170.4935 - val_loss: 168.1820\n", "Epoch 3/3\n", "60000/60000 [==============================] - 12s 200us/step - loss: 166.9137 - val_loss: 165.7955\n" ] } ], "source": [ "vae = Model(inputs=[x, eps], outputs=x_pred, name='vae')\n", "vae.compile(optimizer='rmsprop', loss=nll)\n", "\n", "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n", "x_train = x_train.reshape(-1, original_dim) / 255.\n", "x_test = x_test.reshape(-1, original_dim) / 255.\n", "\n", "hist = vae.fit(\n", " x_train,\n", " x_train,\n", " shuffle=True,\n", " epochs=epochs,\n", " batch_size=batch_size,\n", " validation_data=(x_test, x_test)\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualizing the loss function\n", "\n", "We can automatically visualize the loss function as a function of the epoch using the standard Keras interface for fitting. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "#for pretty plots\n", "golden_size = lambda width: (width, 2. * width / (1 + np.sqrt(5)))\n", "\n", "fig, ax = plt.subplots(figsize=golden_size(6))\n", "\n", "hist_df = pd.DataFrame(hist.history)\n", "hist_df.plot(ax=ax)\n", "\n", "ax.set_ylabel('NELBO')\n", "ax.set_xlabel('# epochs')\n", "\n", "ax.set_ylim(.99*hist_df[1:].values.min(), \n", " 1.1*hist_df[1:].values.max())\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualizing embedding in latent space\n", "\n", "Since our latent space is two dimensional, we can think of our encoder as defining a dimensional reduction of the original 784 dimensional space to just two dimensions! We can visualize the structure of this mapping by plotting the MNIST dataset in the latent space, with each point colored by which number it is $[0,1,\\ldots,9]$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_test_encoded = encoder.predict(x_test, batch_size=batch_size)\n", "plt.figure(figsize=golden_size(6))\n", "plt.scatter(x_test_encoded[:, 0], x_test_encoded[:, 1], c=y_test, cmap='nipy_spectral')\n", "plt.colorbar()\n", "plt.savefig('VAE_MNIST_latent.pdf')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generating new examples\n", "\n", "One of the nice things about VAEs is that they are generative models. Thus, we can generate new examples or fantasy particles much like we did for RBMs and DBMs. We will generate the particles in two different ways\n", "\n", "* Sampling uniformally in the latent space \n", "* Sampling accounting for the fact that the latent space is Gaussian so that we expect most of the data points to be centered around (0,0) and fall off exponentially in all directions. This is done by transforming the uniform grid using the inverse Cumulative Distribution Function (CDF) for the Gaussian.\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# display a 2D manifold of the images\n", "n = 5 # figure with 15x15 images\n", "quantile_min = 0.01\n", "quantile_max = 0.99\n", "\n", "# Linear Sampling\n", "# we will sample n points within [-15, 15] standard deviations\n", "z1_u = np.linspace(5, -5, n)\n", "z2_u = np.linspace(5, -5, n)\n", "z_grid = np.dstack(np.meshgrid(z1_u, z2_u))\n", "\n", "x_pred_grid = decoder.predict(z_grid.reshape(n*n, latent_dim)) \\\n", " .reshape(n, n, img_rows, img_cols)\n", "\n", "# Plot figure\n", "fig, ax = plt.subplots(figsize=golden_size(10))\n", "\n", "ax.imshow(np.block(list(map(list, x_pred_grid))), cmap='gray')\n", "\n", "ax.set_xticks(np.arange(0, n*img_rows, img_rows) + .5 * img_rows)\n", "ax.set_xticklabels(map('{:.2f}'.format, z1_u), rotation=90)\n", "\n", "ax.set_yticks(np.arange(0, n*img_cols, img_cols) + .5 * img_cols)\n", "ax.set_yticklabels(map('{:.2f}'.format, z2_u))\n", "\n", "ax.set_xlabel('$z_1$')\n", "ax.set_ylabel('$z_2$')\n", "ax.set_title('Uniform')\n", "ax.grid(False)\n", "\n", "\n", "plt.savefig('VAE_MNIST_fantasy_uniform.pdf')\n", "plt.show()\n", "\n", "# Inverse CDF sampling\n", "z1 = norm.ppf(np.linspace(quantile_min, quantile_max, n))\n", "z2 = norm.ppf(np.linspace(quantile_max, quantile_min, n))\n", "z_grid2 = np.dstack(np.meshgrid(z1, z2))\n", "\n", "x_pred_grid2 = decoder.predict(z_grid2.reshape(n*n, latent_dim)) \\\n", " .reshape(n, n, img_rows, img_cols)\n", "\n", "# Plot figure Inverse CDF sampling\n", "fig, ax = plt.subplots(figsize=golden_size(10))\n", "\n", "ax.imshow(np.block(list(map(list, x_pred_grid2))), cmap='gray')\n", "\n", "ax.set_xticks(np.arange(0, n*img_rows, img_rows) + .5 * img_rows)\n", "ax.set_xticklabels(map('{:.2f}'.format, z1), rotation=90)\n", "\n", "ax.set_yticks(np.arange(0, n*img_cols, img_cols) + .5 * img_cols)\n", "ax.set_yticklabels(map('{:.2f}'.format, z2))\n", "\n", "ax.set_xlabel('$z_1$')\n", "ax.set_ylabel('$z_2$')\n", "ax.set_title('Inverse CDF')\n", "ax.grid(False)\n", "plt.savefig('VAE_MNIST_fantasy_invCDF.pdf')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "* Play with the standard deviation of the latent variables $\\epsilon$. How does this effect your results?\n", "* Generate samples as you increase the number of latent dimensions. Do your generated samples look better? Visualize the latent variables using a dimensional reduction technique such as PCA or t-SNE. How does it compare to the case with two latent dimensions showed above?\n", "* Repeat this analysis with the supersymmetry dataset? Are the supersymmetric and non-supersymmetric examples separated in the latent dimensions?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python mlreview", "language": "python", "name": "mlreview" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" }, "nikola": { "category": "", "date": "2017-07-21 18:38:07 UTC+10:00", "description": "", "link": "", "slug": "variational-inference-with-implicit-approximate-inference-models-wip-pt-8", "tags": "", "title": "Variational Inference with Implicit Approximate Inference Models (WIP Pt. 8)", "type": "text" } }, "nbformat": 4, "nbformat_minor": 2 }