Variance reduction for dependent sequences with applications to Stochastic Gradient MCMC

TL;DR

This paper introduces a new variance reduction technique for dependent sequences, combining control variates with empirical variance minimization, and demonstrates its effectiveness in improving stochastic gradient MCMC methods for Bayesian inference on large datasets.

Contribution

It proposes a practical variance reduction method that enhances stochastic gradient MCMC by combining control variates with empirical variance minimization, with proven finite-sample properties.

Findings

Significant variance reduction compared to existing methods

Improved Bayesian inference accuracy on benchmark datasets

Moderate computational overhead for enhanced performance

Abstract

In this paper we propose a novel and practical variance reduction approach for additive functionals of dependent sequences. Our approach combines the use of control variates with the minimisation of an empirical variance estimate. We analyse finite sample properties of the proposed method and derive finite-time bounds of the excess asymptotic variance to zero. We apply our methodology to Stochastic Gradient MCMC (SGMCMC) methods for Bayesian inference on large data sets and combine it with existing variance reduction methods for SGMCMC. We present empirical results carried out on a number of benchmark examples showing that our variance reduction method achieves significant improvement as compared to state-of-the-art methods at the expense of a moderate increase of computational overhead.