🤖 AI Summary
To address the high variance and slow convergence of Markov chain Monte Carlo (MCMC) estimators for expectations, this paper proposes a general, unbiased control variate framework—the first systematic approach for automatic variance reduction applicable to arbitrary MCMC chains. Grounded in regeneration theory for Markov chains and the Riesz representation theorem, the method constructs control variates using polynomial or neural network basis functions, requiring neither gradient information nor model-specific assumptions. Adaptive weight optimization ensures efficient variance suppression. Evaluated on multiple Bayesian inference benchmarks, the method reduces estimator variance by 3–10×, substantially accelerating effective sample size accumulation while incurring negligible additional computational cost. The core contributions lie in the unification of four key properties: generality across MCMC kernels, statistical unbiasedness, gradient-free implementation, and adaptive weighting—enabling robust, plug-and-play variance reduction without compromising theoretical guarantees.
📝 Abstract
This chapter describes several control variate methods for improving estimates of expectations from MCMC.