Title: A Divergence Bound for Hybrids of MCMC and Variational Inference and an Application to Langevin Dynamics and SGVI,
Abstract: Two popular classes of methods for approximate inference are Markov chain
Monte Carlo (MCMC) and variational inference. MCMC tends to be accurate if run
for a long enough time, while variational inference tends to give better
approximations at shorter time horizons. However, the amount of time needed for
MCMC to exceed the performance of variational methods can be quite high,
motivating more fine-grained tradeoffs. This paper derives a distribution over
variational parameters, designed to minimize a bound on the divergence between
the resulting marginal distribution and the target, and gives an example of how
to sample from this distribution in a way that interpolates between the
behavior of existing methods based on Langevin dynamics and stochastic gradient
variational inference (SGVI).