Variationally Inferred Sampling Through a Refined Bound for Probabilistic Programs

Abstract: A framework to boost the efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation. We call it the refined variational approximation. Its strength lies both in ease of implementation and automatically tuning of the sampler parameters to speed up mixing time using automatic differentiation. Several strategies to approximate \emph{evidence lower bound} (ELBO) computation are introduced. Experimental evidence of its efficient performance is shown solving an influence diagram in a high-dimensional space using a conditional variational autoencoder (cVAE) as a deep Bayes classifier; an unconditional VAE on density estimation tasks; and state-space models for time-series data.