Matching aggregate posteriors in the variational autoencoder
Surojit Saha Sarang Joshi Ross Whitaker
The variational autoencoder (VAE) is a well-studied, deep, latent-variable
model (DLVM) that efficiently optimizes the variational lower bound of the log
marginal data likelihood and has a strong theoretical foundation. However, the
VAE's known failure to match the aggregate posterior often results in
\emph{pockets/holes} in the latent distribution (i.e., a failure to match the
prior) and/or \emph{posterior collapse}, which is associated with a loss of
information in the latent space. This paper addresses these shortcomings in
VAEs by reformulating the objective function associated with VAEs in order to
match the aggregate/marginal posterior distribution to the prior. We use kernel
density estimate (KDE) to model the aggregate posterior in high dimensions. The
proposed method is named the \emph{aggregate variational autoencoder} (AVAE)
and is built on the theoretical framework of the VAE. Empirical evaluation of
the proposed method on multiple benchmark data sets demonstrates the
effectiveness of the AVAE relative to state-of-the-art (SOTA) methods.