Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
This work addresses the trade-off between speed and accuracy in Bayesian inference for machine learning practitioners, though it appears incremental in bridging existing methods.
The paper tackles the challenge of combining variational inference and Markov Chain Monte Carlo (MCMC) to create a new class of algorithms that offer fast posterior approximation with adjustable accuracy, showing promising initial results.
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.