This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of control variates in reducing variance.

Wedevelop twofundamental tools needed to apply SLC distributions to learning and inference:sampling and mode finding. For sampling we develop an MCMC sampler and give theoretical mixing time bounds.

Many applications require computing likelihoods and marginal probabilities over a distribution defined by a graphical model, tasks which are intractable in general [24].

Work done during an internship at Baidu Inc.

First, wepresent a unified framework that encompasses previous methods.

Forexample,nested MC (NMC) can only achieve, at best, a rate ofO(T 1/3) in the total computational costT [33], comparedwithO(T 1/2)forconventionalMC.