Undirected Graphical Models as Approximate Posteriors

TL;DR

This paper introduces a method to improve variational autoencoders by using undirected graphical models as approximate posteriors, leveraging MCMC-based gradient estimation for training, resulting in better performance than directed models.

Contribution

It develops an efficient training approach for undirected approximate posteriors in VAEs using backpropagation through MCMC updates, enhancing generative quality.

Findings

Undirected models outperform directed graphical models in VAEs.

The proposed gradient estimator enables effective training of discrete VAEs.

Implementation demonstrates improved generative performance.

Abstract

The representation of the approximate posterior is a critical aspect of effective variational autoencoders (VAEs). Poor choices for the approximate posterior have a detrimental impact on the generative performance of VAEs due to the mismatch with the true posterior. We extend the class of posterior models that may be learned by using undirected graphical models. We develop an efficient method to train undirected approximate posteriors by showing that the gradient of the training objective with respect to the parameters of the undirected posterior can be computed by backpropagation through Markov chain Monte Carlo updates. We apply these gradient estimators for training discrete VAEs with Boltzmann machines as approximate posteriors and demonstrate that undirected models outperform previous results obtained using directed graphical models. Our implementation is available at https://github.com/QuadrantAI/dvaess .