Variance reduction for dependent sequences with applications to Stochastic Gradient MCMC

Understand

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.