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.VG acknowledges support from grant FPU16-05034. DRI is grateful to the MINECO MTM2017-86875-C3-1-R project and the AXA-ICMAT Chair in Adversarial Risk Analysis. Both authors acknowledge support from the Severo Ochoa Excellence Program CEX2019-000904-S. This material was based upon work partially supported by the National Science Foundation under Grant DMS-1638521 to the Statistical and Applied Mathematical Sciences Institute as well as a BBVA Foundation project