Markov Chain Monte Carlo and Variational Inference: Bridging the Gap

TL;DR

This paper introduces a new class of inference algorithms that combine variational inference with MCMC steps, enabling flexible, accurate, and efficient Bayesian posterior approximations.

Contribution

It presents a theoretical framework for integrating MCMC into variational inference, bridging the gap between these methods with promising initial results.

Findings

Theoretical foundation for combining MCMC and variational inference.

Algorithms that trade computational cost for increased accuracy.

Initial experiments show promising results.

Abstract

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation. By doing so we obtain a rich class of inference algorithms bridging the gap between variational methods and MCMC, and offering the best of both worlds: fast posterior approximation through the maximization of an explicit objective, with the option of trading off additional computation for additional accuracy. We describe the theoretical foundations that make this possible and show some promising first results.