Variational Inference using Implicit Distributions

TL;DR

This paper explores the use of implicit distributions, particularly GAN-like models, for variational inference, unifying existing methods and proposing new algorithms based on density ratio estimation and contrastive approaches.

Contribution

It provides a unifying review of GAN-based variational inference methods and introduces a flexible framework for developing new algorithms using implicit distributions.

Findings

Connections established between various VI algorithms and GANs

New inference algorithms based on density ratio estimation

Framework enables development of prior-contrastive and joint-contrastive methods

Abstract

Generative adversarial networks (GANs) have given us a great tool to fit implicit generative models to data. Implicit distributions are ones we can sample from easily, and take derivatives of samples with respect to model parameters. These models are highly expressive and we argue they can prove just as useful for variational inference (VI) as they are for generative modelling. Several papers have proposed GAN-like algorithms for inference, however, connections to the theory of VI are not always well understood. This paper provides a unifying review of existing algorithms establishing connections between variational autoencoders, adversarially learned inference, operator VI, GAN-based image reconstruction, and more. Secondly, the paper provides a framework for building new algorithms: depending on the way the variational bound is expressed we introduce prior-contrastive and joint-contrastive methods, and show practical inference algorithms based on either density ratio estimation or denoising.