Asymmetric Variational Autoencoders

Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution. However, freely enriching the family of variational distribution is challenging since the ELBO requires variational likelihood evaluations of the latent variables. In this paper, we propose a novel framework to enrich the variational family by incorporating auxiliary variables to the variational family. The resulting inference network doesn't require density evaluations for the auxiliary variables and thus complex implicit densities over the auxiliary variables can be constructed by neural networks. It can be shown that the actual variational posterior of the proposed approach is essentially modeling a rich probabilistic mixture of simple variational posterior indexed by auxiliary variables, thus a flexible inference model can be built. Empirical evaluations on several density estimation tasks demonstrates the effectiveness of the proposed method.