Variational Bayesian Inference With Stochastic Search

Abstract

Mean-field variational inference is an approximate posterior inference method for Bayesian models. It approximates the full posterior distribution of a model's variables with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate the log joint likelihood of the model with respect to the factorized approximation. Often not all integrals are closed-form, which is traditionally handled using lower bound approximations. We present an algorithm based on stochastic optimization that allows for direct optimization of the variational lower bound in all models. This method uses control variates for variance reduction of the stochastic search gradient, in which existing lower bounds can play an important role. We demonstrate the approach on logistic regression and the hierarchical Dirichlet process.