{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/dev/latent-variable-models/latent_variable_models_part_2.ipynb)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"try:\n",
" # Use Tensorflow 2.x\n",
" %tensorflow_version 2.x\n",
" # Check if notebook is running in Google Colab\n",
" import google.colab\n",
"except:\n",
" pass"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Latent variable models, part 2: Stochastic variational inference and variational autoencoders\n",
"\n",
"[Part 1](latent_variable_models_part_1.ipynb) of this article series introduced a latent variable model with discrete latent variables, the Gaussian mixture model (GMM), and an algorithm to fit this model to data, the EM algorithm. Part 2 covers a latent variable model with continuous latent variables for modeling more complex data, like natural images for example, and a Bayesian inference technique that can be used in conjunction with stochastic optimization algorithms.\n",
"\n",
"Consider a natural image of size $100 \\times 100$ with a single channel. This image is a point in $10.000$-dimensional space. Natural images are usually not uniformly distributed in this space but reside on a much lower-dimensional manifold within this high-dimensional space. The lower dimensionality of the manifold is related to the limited degrees of freedom in these images e.g. only a limited number of pixel value combinations are actually perceived as natural images. \n",
"\n",
"Modeling natural images with latent variable models whose continuous latent variables represent locations on the manifold can be a useful approach that is also discussed here. As in part 1, a model with one latent variable $\\mathbf{t}_i$ per observation $\\mathbf{x}_i$ is used but now the latent variables are continuous rather than discrete variables. Therefore, summations over latent variable states are now replaced by integrals and these are often intractable for more complex models. \n",
"\n",
"Observations i.e. images $\\mathbf{X} = \\left\\{ \\mathbf{x}_1, \\ldots, \\mathbf{x}_N \\right\\}$ are again described with a probabilistic model $p(\\mathbf{x} \\lvert \\boldsymbol{\\theta})$. Goal is to maximize the data likelihood $p(\\mathbf{X} \\lvert \\boldsymbol{\\theta})$ w.r.t. $\\boldsymbol{\\theta}$ and to obtain approximate posterior distributions over continuous latent variables. The joint distribution over an observed variable $\\mathbf{x}$ and a latent variable $\\mathbf{t}$ is defined as the product of the conditional distribution over $\\mathbf{x}$ given $\\mathbf{t}$ and the prior distribution over $\\mathbf{t}$.\n",
"\n",
"$$\n",
"p(\\mathbf{x}, \\mathbf{t} \\lvert \\boldsymbol{\\theta}) = p(\\mathbf{x} \\lvert \\mathbf{t}, \\boldsymbol{\\theta}) p(\\mathbf{t} \\lvert \\boldsymbol{\\theta})\n",
"\\tag{1}\n",
"$$\n",
"\n",
"We obtain the marginal distribution over x by integrating over t.\n",
"\n",
"$$\n",
"p(\\mathbf{x} \\lvert \\boldsymbol{\\theta}) = \\int p(\\mathbf{x} \\lvert \\mathbf{t}, \\boldsymbol{\\theta}) p(\\mathbf{t} \\lvert \\boldsymbol{\\theta}) d\\mathbf{t}\n",
"\\tag{2}\n",
"$$\n",
"\n",
"This integral is usually intractable for even moderately complex conditional probabilities $p(\\mathbf{x} \\lvert \\mathbf{t}, \\boldsymbol{\\theta})$ and consequently also the true posterior.\n",
"\n",
"$$\n",
"p(\\mathbf{t} \\lvert \\mathbf{x}, \\boldsymbol{\\theta}) = {{p(\\mathbf{x} \\lvert \\mathbf{t}, \\boldsymbol{\\theta}) p(\\mathbf{t} \\lvert \\boldsymbol{\\theta})} \\over {p(\\mathbf{x} \\lvert \\boldsymbol{\\theta})}}\n",
"\\tag{3}\n",
"$$\n",
"\n",
"This means that the E-step of the EM algorithm becomes intractable. Recall from part 1 that the lower bound of the log marginal likelihood is given by \n",
"\n",
"$$\n",
"\\mathcal{L}(\\boldsymbol{\\theta}, q) = \\log p(\\mathbf{X} \\lvert \\boldsymbol{\\theta}) - \\mathrm{KL}(q(\\mathbf{T} \\lvert \\mathbf{X}) \\mid\\mid p(\\mathbf{T} \\lvert \\mathbf{X}, \\boldsymbol{\\theta}))\n",
"\\tag{4}\n",
"$$\n",
"\n",
"In the E-step, the lower bound is maximized w.r.t. $q$ and $\\boldsymbol{\\theta}$ is held fixed. If the true posterior is tractable, we can set $q$ to the true posterior so that the KL divergence becomes $0$ which maximizes the lower bound for the current value of $\\boldsymbol{\\theta}$. If the true posterior is intractable approximations must be used. \n",
"\n",
"Here, we will use *stochastic variational inference*, a Bayesian inference method that also scales to large datasets[1]. Numerous other approximate inference approaches exist but these are not discussed here to keep the article focused.\n",
"\n",
"## Stochastic variational inference\n",
"\n",
"The field of mathematics that covers the optimization of a functional w.r.t. a function, like ${\\mathrm{argmax}}_q \\mathcal{L}(\\boldsymbol{\\theta}, q)$ in our example, is the [calculus of variations](https://en.wikipedia.org/wiki/Calculus_of_variations), hence the name *variational inference*. In this context, $q$ is called a *variational distribution* and $\\mathcal{L}(\\boldsymbol{\\theta}, q)$ a *variational lower bound*. \n",
"\n",
"We will approximate the true posterior with a parametric variational distribution $q(\\mathbf{t} \\lvert \\mathbf{x}, \\boldsymbol{\\phi})$ and try to find a value of $\\boldsymbol{\\phi}$ that minimizes the KL divergence between this distribution and the true posterior. Using $q(\\mathbf{t} \\lvert \\mathbf{x}, \\boldsymbol{\\phi})$ we can formulate the variational lower bound for a single observation $\\mathbf{x}_i$ as\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\mathcal{L}(\\boldsymbol{\\theta}, q; \\mathbf{x}_i) &=\n",
"\\log p(\\mathbf{x}_i \\lvert \\boldsymbol{\\theta}) - \\mathrm{KL}(q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\mid\\mid p(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\theta})) \\\\ &= \n",
"\\log p(\\mathbf{x}_i \\lvert \\boldsymbol{\\theta}) - \\int q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\log {{q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})} \\over {p(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\theta})}} d\\mathbf{t}_i \\\\ &= \n",
"\\int q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\log {{p(\\mathbf{x}_i \\lvert \\boldsymbol{\\theta}) p(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\theta})} \\over {q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})}} d\\mathbf{t}_i \\\\ &= \n",
"\\int q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\log {{p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta}) p(\\mathbf{t}_i \\lvert \\boldsymbol{\\theta})} \\over {q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})}} d\\mathbf{t}_i \\\\ &=\n",
"\\int q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta}) d\\mathbf{t}_i - \\mathrm{KL}(q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\mid\\mid p(\\mathbf{t}_i \\lvert \\boldsymbol{\\theta})) \\\\ &=\n",
"\\mathbb{E}_{q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})} \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta}) - \\mathrm{KL}(q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\mid\\mid p(\\mathbf{t}_i \\lvert \\boldsymbol{\\theta})) \n",
"\\end{align*}\n",
"\\tag{5}\n",
"$$\n",
"\n",
"We assume that the integral $\\int q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta}) d\\mathbf{t}_i$ is intractable but we can choose a functional form of $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$ from which we can easily sample so that the expectation of $\\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta})$ w.r.t. to $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$ can be approximated with $L$ samples from $q$. \n",
"\n",
"$$\n",
"\\mathcal{L}(\\boldsymbol{\\theta}, q; \\mathbf{x}_i) \\approx {1 \\over L} \\sum_{l=1}^L \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_{i,l}, \\boldsymbol{\\theta}) - \\mathrm{KL}(q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\mid\\mid p(\\mathbf{t}_i \\lvert \\boldsymbol{\\theta}))\n",
"\\tag{6}\n",
"$$\n",
"\n",
"where $\\mathbf{t}_{i,l} \\sim q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$. We will also choose the functional form of $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$ and $p(\\mathbf{t}_i \\lvert \\boldsymbol{\\theta})$ such that integration of the KL divergence can be done analytically, hence, no samples are needed to evaluate the KL divergence. With these choices, an approximate evaluation of the variational lower bound is possible. But in order to optimize the lower bound w.r.t. $\\boldsymbol{\\theta}$ and $\\boldsymbol{\\phi}$ we need to approximate the gradients w.r.t. these parameters.\n",
"\n",
"### Stochastic gradients\n",
"\n",
"We first assume that the analytical expression of the KL divergence, the second term on the RHS of Eq. $(5)$, is differentiable w.r.t. $\\boldsymbol{\\phi}$ and $\\boldsymbol{\\theta}$ so that deterministic gradients can be computed. The gradient of the first term on the RHS of Eq. $(5)$ w.r.t. $\\boldsymbol{\\theta}$ is\n",
"\n",
"$$\n",
"\\nabla_{\\boldsymbol{\\theta}} \\mathbb{E}_{q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})} \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta}) =\n",
"\\mathbb{E}_{q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})} \\nabla_{\\boldsymbol{\\theta}} \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta})\n",
"\\tag{7}\n",
"$$\n",
"\n",
"Here, $\\nabla_{\\boldsymbol{\\theta}}$ can be moved inside the expectation as $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$ doesn't depend on $\\boldsymbol{\\theta}$. Assuming that $p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta})$ is differentiable w.r.t. $\\boldsymbol{\\theta}$, unbiased estimates of the gradient can be obtained by sampling from $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$.\n",
"\n",
"$$\n",
"\\nabla_{\\boldsymbol{\\theta}} \\mathbb{E}_{q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})} \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta}) \\approx \n",
"{1 \\over L} \\sum_{l=1}^L \\nabla_{\\boldsymbol{\\theta}} \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_{i,l}, \\boldsymbol{\\theta})\n",
"\\tag{8}\n",
"$$\n",
"\n",
"We will later implement $p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta})$ as neural network and use Tensorflow to compute $\\nabla_{\\boldsymbol{\\theta}} \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_{i,l}, \\boldsymbol{\\theta})$. The gradient w.r.t. $\\boldsymbol{\\phi}$ is a bit more tricky as $\\nabla_{\\boldsymbol{\\phi}}$ cannot be moved inside the expectation because $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$ depends on $\\boldsymbol{\\phi}$. But if we can decompose $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$ into an auxiliary distribution $p(\\boldsymbol\\epsilon)$ that doesn't depend on $\\boldsymbol{\\phi}$ and a deterministic, differentiable function $g(\\boldsymbol\\epsilon, \\mathbf{x}, \\boldsymbol{\\phi})$ where $\\mathbf{t}_i = g(\\boldsymbol\\epsilon, \\mathbf{x}_i, \\boldsymbol{\\phi})$ and $\\boldsymbol\\epsilon \\sim p(\\boldsymbol\\epsilon)$ then we can re-formulate the gradient w.r.t. $\\boldsymbol{\\phi}$ as\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\nabla_{\\boldsymbol{\\phi}} \\mathbb{E}_{q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})} \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta}) &=\n",
"\\nabla_{\\boldsymbol{\\phi}} \\mathbb{E}_{p(\\boldsymbol\\epsilon)} \\log p(\\mathbf{x}_i \\lvert g(\\boldsymbol\\epsilon, \\mathbf{x}_i, \\boldsymbol{\\phi}), \\boldsymbol{\\theta}) \\\\ &=\n",
"\\mathbb{E}_{p(\\boldsymbol\\epsilon)} \\nabla_{\\boldsymbol{\\phi}} \\log p(\\mathbf{x}_i \\lvert g(\\boldsymbol\\epsilon, \\mathbf{x}_i, \\boldsymbol{\\phi}), \\boldsymbol{\\theta})\n",
"\\tag{9}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"Unbiased estimates of the gradient w.r.t. $\\boldsymbol{\\phi}$ can then be obtained by sampling from $p(\\boldsymbol\\epsilon)$.\n",
"\n",
"$$\n",
"\\nabla_{\\boldsymbol{\\phi}} \\mathbb{E}_{q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})} \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta}) \\approx\n",
"{1 \\over L} \\sum_{l=1}^L \\nabla_{\\boldsymbol{\\phi}} \\log p(\\mathbf{x}_i \\lvert \\mathbf{t}_{i,l}, \\boldsymbol{\\theta})\n",
"\\tag{10}\n",
"$$\n",
"\n",
"\n",
"where $\\mathbf{t}_{i,l} = g(\\boldsymbol\\epsilon_l, \\mathbf{x}_i, \\boldsymbol{\\phi})$ and $\\boldsymbol\\epsilon_l \\sim p(\\boldsymbol\\epsilon)$. This so-called *reparameterization trick* can be applied to a wide range of probability distributions, including Gaussian distributions. Furthermore, stochastic gradients w.r.t. $\\boldsymbol{\\phi}$ obtained with this trick have much smaller variance than those obtained with alternative approaches (not shown here).\n",
"\n",
"### Mini-batches\n",
"\n",
"The above approximations for the variational lower bound and its gradients have been formulated for a single training example $\\mathbf{x}_i$ but this can be easily extended to mini-batches $\\mathbf{X}^M = \\left\\{ \\mathbf{x}_1, \\ldots, \\mathbf{x}_M \\right\\}$ with $M$ random samples from a dataset $\\mathbf{X}$ of $N$ i.i.d. observations. The lower bound of the full dataset $\\mathcal{L}(\\boldsymbol{\\theta}, q; \\mathbf{X})$ can then be approximated as\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\mathcal{L}(\\boldsymbol{\\theta}, q; \\mathbf{X}) &\\approx\n",
"{N \\over M} \\sum_{i=1}^M \\mathcal{L}(\\boldsymbol{\\theta}, q; \\mathbf{x}_i) \\\\ &=\n",
"\\mathcal{L}^M(\\boldsymbol{\\theta}, q; \\mathbf{X}^M)\n",
"\\tag{11}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"Gradients of $\\mathcal{L}^M(\\boldsymbol{\\theta}, q; \\mathbf{X}^M)$ can be obtained as described above together with averaging over the mini-batch and used in combination with optimizers like Adam, for example, to update the parameters of the latent variable model. Sampling from the variational distribution $q$ and usage of mini-batches leads to noisy gradients, hence the term *stochastic variational inference*. \n",
"\n",
"If $M$ is sufficiently large, for example $M = 100$, then $L$ can be even set to $1$ i.e. a single sample from the variational distribution per training example is sufficient to get a good gradient estimate on average.\n",
"\n",
"## Variational autoencoder\n",
"\n",
"From the perspective of a generative model, $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$ is a probabilistic *encoder* because it generates a *latent code* $\\mathbf{t}_i$ for input image $\\mathbf{x}_i$ and $p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta})$ is a probabilistic *decoder* because it generates or reconstructs an image $\\mathbf{x}_i$ from latent code $\\mathbf{t}_i$. Optimizing the variational lower bound w.r.t. parameters $\\boldsymbol{\\theta}$ and $\\boldsymbol{\\phi}$ can therefore be regarded as training a probabilistic autoencoder or *variational autoencoder* (VAE)[1].\n",
"\n",
"In this context, the first term on the RHS of Eq. $(5)$ can be interpreted as expected negative *reconstruction error*. The second term is a *regularization term* that encourages the variational distribution to be close to the prior over latent variables. If the regularization term is omitted, the variational distribution would collapse to a delta function and the variational autoencoder would degenerate to a \"usual\" deterministic autoencoder. \n",
"\n",
"### Implementation\n",
"\n",
"For implementing a variational autoencoder, we make the following choices:\n",
"\n",
"- The variational distribution $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$ is a multivariate Gaussian $\\mathcal{N}(\\mathbf{t}_i \\lvert \\boldsymbol\\mu(\\mathbf{x}_i, \\boldsymbol{\\phi}), \\boldsymbol\\sigma^2(\\mathbf{x}_i, \\boldsymbol{\\phi}))$ with a diagonal covariance matrix where mean vector $\\boldsymbol\\mu$ and the covariance diagonal $\\boldsymbol\\sigma^2$ are functions of $\\mathbf{x}_i$ and $\\boldsymbol{\\phi}$. These functions are implemented as neural network and learned during optimization of the lower bound w.r.t. $\\boldsymbol{\\phi}$. After reparameterization, samples from $q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi})$ are obtained via the deterministic function $g(\\boldsymbol\\epsilon, \\mathbf{x}_i, \\boldsymbol{\\phi}) = \\boldsymbol\\mu(\\mathbf{x}_i, \\boldsymbol{\\phi}) + \\boldsymbol\\sigma^2(\\mathbf{x}_i, \\boldsymbol{\\phi}) \\odot \\boldsymbol\\epsilon$ and an auxiliary distribution $p(\\boldsymbol\\epsilon) = \\mathcal{N}(\\boldsymbol\\epsilon \\lvert \\mathbf{0}, \\mathbf{I})$.\n",
"\n",
"- The conditional distribution $p(\\mathbf{x}_i \\lvert \\mathbf{t}_i, \\boldsymbol{\\theta})$ is a multivariate Bernoulli distribution $\\text{Ber}(\\mathbf{x}_i \\lvert \\mathbf{k}(\\mathbf{t}_i, \\boldsymbol{\\theta}))$ where parameter $\\mathbf{k}$ is a function of $\\mathbf{t}_i$ and $\\boldsymbol{\\theta}$. This distribution models the binary training data i.e. monochrome (= binarized) MNIST images in our example. Function $\\mathbf{k}$ computes for each pixel its expected value. It is also implemented as neural network and learned during optimization of the lower bound w.r.t. $\\boldsymbol{\\theta}$. Taking the (negative) logarithm of $\\text{Ber}(\\mathbf{x}_i \\lvert \\mathbf{k}(\\mathbf{t}_i, \\boldsymbol{\\theta}))$ gives a sum over pixel-wise binary cross entropies as shown in Eq. $(12)$\n",
"\n",
"- Prior $p(\\mathbf{t}_i \\lvert \\boldsymbol{\\theta})$ is a multivariate Gaussian distribution $\\mathcal{N}(\\mathbf{t}_i \\lvert \\mathbf{0}, \\mathbf{I})$ with zero mean and unit covariance matrix. With the chosen functional forms of the prior and the variational distribution $q$, $\\mathrm{KL}(q(\\mathbf{t}_i \\lvert \\mathbf{x}_i, \\boldsymbol{\\phi}) \\mid\\mid p(\\mathbf{t}_i \\lvert \\boldsymbol{\\theta}))$ can be integrated analytically to $-{1 \\over 2} \\sum_{d=1}^D (1 + \\log \\sigma_{i,d}^2 - \\mu_{i,d}^2 - \\sigma_{i,d}^2)$ where $D$ is the dimensionality of the latent space and $\\mu_{i,d}$ and $\\sigma_{i,d}$ is the $d$-th element of $\\boldsymbol\\mu(\\mathbf{x}_i, \\boldsymbol{\\phi})$ and $\\boldsymbol\\sigma(\\mathbf{x}_i, \\boldsymbol{\\phi})$, respectively.\n",
"\n",
"Using these choices and setting $L = 1$, the variational lower bound for a single image $\\mathbf{x}_i$ can be approximated as\n",
"\n",
"$$\n",
"\\mathcal{L}(\\boldsymbol{\\theta}, q; \\mathbf{x}_i) \\approx \n",
"- \\sum_c \\left(x_{i,c} \\log k_{i,c} + (1 - x_{i,c}) \\log (1 - k_{i,c})\\right) + {1 \\over 2} \\sum_d (1 + \\log \\sigma_{i,d}^2 - \\mu_{i,d}^2 - \\sigma_{i,d}^2)\n",
"\\tag{12}\n",
"$$\n",
"\n",
"where $x_{i,c}$ is the value of pixel $c$ in image $\\mathbf{x}_i$ and $k_{i,c}$ its expected value. The negative value of the lower bound is used as loss during training. The following figure outlines the architecture of the variational autoencoder. \n",
"\n",
"![VAE](images/vae/auto-encoder.jpg)\n",
"\n",
"The definitions of the encoder and decoder neural networks were taken from \\[2\\]. Here, the encoder computes the logarithm of the variance, instead of the variance directly, for reasons of numerical stability. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from tensorflow.keras import layers\n",
"from tensorflow.keras.models import Model\n",
"\n",
"\n",
"def create_encoder(latent_dim):\n",
" \"\"\"\n",
" Creates a convolutional encoder for MNIST images.\n",
"\n",
" Args:\n",
" latent_dim: dimensionality of latent space.\n",
" \"\"\"\n",
" encoder_iput = layers.Input(shape=(28, 28, 1))\n",
" \n",
" x = layers.Conv2D(32, 3, padding='same', activation='relu')(encoder_iput)\n",
" x = layers.Conv2D(64, 3, padding='same', activation='relu', strides=(2, 2))(x)\n",
" x = layers.Conv2D(64, 3, padding='same', activation='relu')(x)\n",
" x = layers.Conv2D(64, 3, padding='same', activation='relu')(x)\n",
" x = layers.Flatten()(x)\n",
" x = layers.Dense(32, activation='relu')(x)\n",
"\n",
" q_mean = layers.Dense(latent_dim)(x)\n",
" q_log_var = layers.Dense(latent_dim)(x)\n",
"\n",
" return Model(encoder_iput, [q_mean, q_log_var], name='encoder')\n",
"\n",
"\n",
"def create_decoder(latent_dim):\n",
" \"\"\"\n",
" Creates a convolutional decoder for MNIST images.\n",
"\n",
" Args:\n",
" latent_dim: dimensionality of latent space.\n",
" \"\"\"\n",
" decoder_input = layers.Input(shape=(latent_dim,))\n",
" \n",
" x = layers.Dense(12544, activation='relu')(decoder_input)\n",
" x = layers.Reshape((14, 14, 64))(x)\n",
" x = layers.Conv2DTranspose(32, 3, padding='same', activation='relu', strides=(2, 2))(x)\n",
" k = layers.Conv2D(1, 3, padding='same', activation='sigmoid')(x)\n",
" \n",
" return Model(decoder_input, k, name='decoder')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These definitions are used to implement a `VariationalAutoencoder` model class."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import tensorflow as tf\n",
"\n",
"class VariationalAutoencoder(Model):\n",
" def __init__(self, latent_dim=2):\n",
" \"\"\"\n",
" Creates a variational autoencoder Keras model.\n",
" \n",
" Args:\n",
" latent_dim: dimensionality of latent space.\n",
" \"\"\"\n",
" super().__init__()\n",
" self.latent_dim = latent_dim\n",
" self.encoder = create_encoder(latent_dim)\n",
" self.decoder = create_decoder(latent_dim)\n",
" \n",
" def encode(self, x):\n",
" \"\"\"\n",
" Computes variational distribution q statistics from \n",
" input image x.\n",
" \n",
" Args:\n",
" x: input image, shape (M, 28, 28, 1).\n",
" \n",
" Returns:\n",
" Mean, shape (M, latent_dim), and log variance, \n",
" shape (M, latent_dim), of multivariate Gaussian \n",
" distribution q. \n",
" \"\"\"\n",
" q_mean, q_log_var = self.encoder(x)\n",
" return q_mean, q_log_var\n",
" \n",
" def sample(self, q_mean, q_log_var):\n",
" \"\"\"\n",
" Samples latent code from variational distribution q.\n",
" \n",
" Args:\n",
" q_mean: mean of q, shape (M, latent_dim).\n",
" q_log_var: log variance of q, shape (M, latent_dim).\n",
" \n",
" Returns:\n",
" Latent code sample, shape (M, latent_dim).\n",
" \"\"\"\n",
" eps = tf.random.normal(shape=q_mean.shape)\n",
" return q_mean + tf.exp(q_log_var * .5) * eps\n",
" \n",
" def decode(self, t):\n",
" \"\"\"\n",
" Computes expected pixel values (= probabilities k) from \n",
" latent code t.\n",
" \n",
" Args:\n",
" t: latent code, shape (M, latent_dim).\n",
"\n",
" Returns:\n",
" Probabilities k of multivariate Bernoulli \n",
" distribution p, shape (M, 28, 28, 1).\n",
" \"\"\"\n",
" k = self.decoder(t)\n",
" return k\n",
" \n",
" def call(self, x):\n",
" \"\"\"\n",
" Computes expected pixel values (= probabilities k) of a \n",
" reconstruction of input image x. \n",
" \n",
" Args:\n",
" x: input image, shape (M, 28, 28, 1).\n",
"\n",
" Returns:\n",
" Probabilities k of multivariate Bernoulli \n",
" distribution p, shape (M, 28, 28, 1).\n",
" \"\"\"\n",
" q_mean, q_log_var = self.encode(x)\n",
" t = self.sample(q_mean, q_log_var)\n",
" return self.decode(t)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `variational_lower_bound` function is implemented using Eq. $(12)$ and Eq. $(11)$ but instead of estimating the lower bound for the full dataset it is normalized by the dataset size $N$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from tensorflow.keras.losses import binary_crossentropy\n",
"\n",
"def variational_lower_bound(model, x):\n",
" \"\"\"\n",
" Computes normalized variational lower bound.\n",
" \n",
" Args:\n",
" x: input images, shape (M, 28, 28, 1)\n",
" \n",
" Returns:\n",
" Variational lower bound averaged over M \n",
" samples in batch and normalized by dataset\n",
" size N.\n",
" \"\"\"\n",
" q_mean, q_log_var = model.encode(x)\n",
" t = model.sample(q_mean, q_log_var)\n",
" x_rc = model.decode(t)\n",
" \n",
" # Expected negative reconstruction error\n",
" neg_rc_error = -tf.reduce_sum(binary_crossentropy(x, x_rc), axis=[1, 2])\n",
"\n",
" # Regularization term (negative KL divergence)\n",
" neg_kl_div = 0.5 * tf.reduce_sum(1 + q_log_var \\\n",
" - tf.square(q_mean) \\\n",
" - tf.exp(q_log_var), axis=-1)\n",
" \n",
" # Average over mini-batch (of size M)\n",
" return tf.reduce_mean(neg_rc_error + neg_kl_div)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The training procedure uses the negative value of the variational lower bound as loss to compute stochastic gradient estimates. These are used by the `optimizer` to update model parameters $\\boldsymbol\\theta$ and $\\boldsymbol\\phi$. The normalized variational lower bound of the test set is computed at the end of each epoch and printed."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"@tf.function\n",
"def train_step(model, optimizer, x):\n",
" \"\"\"Trains VAE on mini-batch x using optimizer.\n",
" \"\"\"\n",
" with tf.GradientTape() as tape:\n",
" # Compute neg. variational lower bound as loss\n",
" loss = -variational_lower_bound(model, x)\n",
" # Compute gradients from neg. variational lower bound\n",
" gradients = tape.gradient(loss, model.trainable_variables)\n",
" # Apply gradients to model parameters theta and phi\n",
" optimizer.apply_gradients(zip(gradients, model.trainable_variables))\n",
" return loss\n",
" \n",
"def train(model, optimizer, ds_train, ds_test, epochs):\n",
" \"\"\"Trains VAE on training dataset ds_train using \n",
" optimizer for given number of epochs.\n",
" \"\"\"\n",
" for epoch in range(1, epochs + 1):\n",
" for x in ds_train:\n",
" train_step(model, optimizer, x)\n",
" \n",
" vlb_mean = tf.keras.metrics.Mean()\n",
" for x in ds_test:\n",
" vlb_mean(variational_lower_bound(model, x))\n",
" vlb = vlb_mean.result()\n",
" print(f'Epoch: {epoch:02d}, Test set VLB: {vlb:.2f}')\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since the data are modelled with a multivariate Bernoulli distribution, the MNIST images are first binarized to monochrome images so that their pixel values are either 0 or 1. The training batch size is set to 100 to get reliable stochastic gradient estimates."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"from tensorflow.keras.datasets import mnist\n",
"\n",
"(x_train, _), (x_test, y_test) = mnist.load_data()\n",
"\n",
"x_train = (x_train > 127.5).astype('float32') # binarize\n",
"x_train = x_train.reshape(-1, 28, 28, 1)\n",
"\n",
"x_test = (x_test > 127.5).astype('float32') # binarize\n",
"x_test = x_test.reshape(-1, 28, 28, 1)\n",
"\n",
"batch_size = 100\n",
"\n",
"ds_train = tf.data.Dataset.from_tensor_slices(x_train).shuffle(x_train.shape[0]).batch(batch_size)\n",
"ds_test = tf.data.Dataset.from_tensor_slices(x_test).shuffle(x_test.shape[0]).batch(batch_size)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We choose a two-dimensional latent space so that it can be easily visualized. Training the variational autoencoder with `RMSProp` as optimizer at a learning rate of `1e-3` for 20 epochs gives already reasonable results. This takes a few minutes on a single GPU."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"vae = VariationalAutoencoder(latent_dim=2)\n",
"opt = tf.keras.optimizers.RMSprop(lr=1e-3)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch: 01, Test set VLB: -166.56\n",
"Epoch: 02, Test set VLB: -158.25\n",
"Epoch: 03, Test set VLB: -154.44\n",
"Epoch: 04, Test set VLB: -152.20\n",
"Epoch: 05, Test set VLB: -150.47\n",
"Epoch: 06, Test set VLB: -148.30\n",
"Epoch: 07, Test set VLB: -148.63\n",
"Epoch: 08, Test set VLB: -146.66\n",
"Epoch: 09, Test set VLB: -145.61\n",
"Epoch: 10, Test set VLB: -147.64\n",
"Epoch: 11, Test set VLB: -148.42\n",
"Epoch: 12, Test set VLB: -143.86\n",
"Epoch: 13, Test set VLB: -143.31\n",
"Epoch: 14, Test set VLB: -145.67\n",
"Epoch: 15, Test set VLB: -143.78\n",
"Epoch: 16, Test set VLB: -143.29\n",
"Epoch: 17, Test set VLB: -142.25\n",
"Epoch: 18, Test set VLB: -142.99\n",
"Epoch: 19, Test set VLB: -143.39\n",
"Epoch: 20, Test set VLB: -143.31\n"
]
}
],
"source": [
"train(model=vae, \n",
" optimizer=opt, \n",
" ds_train=ds_train, \n",
" ds_test=ds_test, \n",
" epochs=20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following figure shows the locations of test set images in latent space. Here, the mean vectors of the variational distributions are plotted. The latent space is organized by structural similarity of digits i.e. structurally similar digits have a smaller distance in latent space than structurally dissimilar digits. For example, digits 4 and 9 usually differ only by a horizontal bar or curve at the top of the image and are therefore in proximity."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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