Variational Bayesian Inference with Stochastic Search

TL;DR

This paper introduces a stochastic optimization algorithm for variational Bayesian inference that directly maximizes the lower bound, using control variates to improve gradient estimates, applicable to non-conjugate models.

Contribution

It presents a novel stochastic search method for variational inference that handles non-conjugate models without relying solely on lower bounds.

Findings

Effective on logistic regression and HDP approximation

Reduces variance of stochastic gradients

Enables direct optimization of variational lower bound

Abstract

Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate a sum of terms in the log joint likelihood using this factorized distribution. Often not all integrals are in closed form, which is typically handled by using a lower bound. We present an alternative algorithm based on stochastic optimization that allows for direct optimization of the variational lower bound. This method uses control variates to reduce the variance of the stochastic search gradient, in which existing lower bounds can play an important role. We demonstrate the approach on two non-conjugate models: logistic regression and an approximation to the HDP.