Generalizing Variational Autoencoders with Hierarchical Empirical Bayes

TL;DR

This paper introduces HEBAE, a hierarchical Bayesian autoencoder that improves latent space modeling and sample quality in VAEs by adaptively balancing regularization and reconstruction, demonstrating superior results on MNIST and CelebA.

Contribution

The paper proposes a hierarchical prior framework for VAEs, enhancing robustness and sample quality by better managing the regularization-reconstruction trade-off.

Findings

HEBAE outperforms existing autoencoder methods in FID scores.

HEBAE is more robust to hyperparameter variations.

It produces higher quality samples on MNIST and CelebA.

Abstract

Variational Autoencoders (VAEs) have experienced recent success as data-generating models by using simple architectures that do not require significant fine-tuning of hyperparameters. However, VAEs are known to suffer from over-regularization which can lead to failure to escape local maxima. This phenomenon, known as posterior collapse, prevents learning a meaningful latent encoding of the data. Recent methods have mitigated this issue by deterministically moment-matching an aggregated posterior distribution to an aggregate prior. However, abandoning a probabilistic framework (and thus relying on point estimates) can both lead to a discontinuous latent space and generate unrealistic samples. Here we present Hierarchical Empirical Bayes Autoencoder (HEBAE), a computationally stable framework for probabilistic generative models. Our key contributions are two-fold. First, we make gains by placing a hierarchical prior over the encoding distribution, enabling us to adaptively balance the trade-off between minimizing the reconstruction loss function and avoiding over-regularization. Second, we show that assuming a general dependency structure between variables in the latent space produces better convergence onto the mean-field assumption for improved posterior inference. Overall, HEBAE is more robust to a wide-range of hyperparameter initializations than an analogous VAE. Using data from MNIST and CelebA, we illustrate the ability of HEBAE to generate higher quality samples based on FID score than existing autoencoder-based approaches.