Auxiliary Variational MCMC

Abstract

We introduce Auxiliary Variational MCMC, a novel framework for learning MCMC kernels that combines recent advances in variational inference with insights drawn from traditional auxiliary variable MCMC methods such as Hamiltonian Monte Carlo. Our framework exploits low dimensional structure in the target distribution in order to learn a more efficient MCMC sampler. The resulting sampler is able to suppress random walk behaviour and mix between modes efficiently, without the need to compute gradients of the target distribution. We test our sampler on a number of challenging distributions, where the underlying structure is known, and on the task of posterior sampling in Bayesian logistic regression. Code to reproduce all experiments is available at https://github.com/AVMCMC/AuxiliaryVariationalMCMC .