Variationally Inferred Sampling through a Refined Bound

In this work, a framework to boost the efficiency of Bayesian inference in probabilistic models is introduced by embedding a Markov chain sampler within a variational posterior approximation. We call this framework refined variational approximation. Its strengths are its ease of implementation and the automatic tuning of sampler parameters, leading to a faster mixing time through automatic differentiation. Several strategies to approximate evidence lower bound (ELBO) computation are also introduced. Its efficient performance is showcased experimentally using state-space models for time-series data, a variational encoder for density estimation and a conditional variational autoencoder as a deep Bayes classifier.

Automated summary

This work introduces a framework to enhance the efficiency of Bayesian inference by embedding a Markov chain sampler within a variational posterior approximation, termed as refined variational approximation. The framework's strengths lie in its ease of implementation, automatic tuning of sampler parameters, and faster mixing time through automatic differentiation. Experimental results demonstrate its efficient performance in state-space models, variational encoder, and conditional variational autoencoder.