Variationally Inferred Sampling Through a Refined Bound for Probabilistic Programs

A framework to boost efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation, which we call the refined variational approximation. Its strength lies both in ease of implementation and in automatically tuning the sampler parameters to speed up mixing time. Several strategies to approximate the \emph{evidence lower bound} (ELBO) computation are introduced, including a rewriting of the ELBO objective. A specialization towards state-space models is proposed. Experimental evidence of its efficient performance is shown by 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.