Matching aggregate posteriors in the variational autoencoder
This addresses a known problem in VAEs for researchers and practitioners in deep generative modeling, offering an incremental improvement.
The paper tackles the variational autoencoder's failure to match the aggregate posterior, which causes issues like latent space holes and posterior collapse, by reformulating the objective to match the aggregate posterior to the prior using kernel density estimation, resulting in the AVAE method that shows effectiveness on benchmark datasets relative to state-of-the-art methods.
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.