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Regularized Zero-Variance Control Variates

Lookup NU author(s): Professor Chris Oates

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Abstract

© 2023 International Society for Bayesian Analysis. Zero-variance control variates (ZV-CV) are a post-processing method to reduce the variance of Monte Carlo estimators of expectations using the derivatives of the log target. Once the derivatives are available, the only additional computational effort lies in solving a linear regression problem. Significant variance reductions have been achieved with this method in low dimensional examples, but the number of covariates in the regression rapidly increases with the dimension of the target. In this paper, we present compelling empirical evidence that the use of penalized regression techniques in the selection of high-dimensional control variates provides performance gains over the classical least squares method. Another type of regularization based on using subsets of derivatives, or a priori regularization as we refer to it in this paper, is also proposed to reduce computational and storage requirements. Several examples showing the utility and limitations of regularized ZV-CV for Bayesian inference are given. The methods proposed in this paper are accessible through the R package ZVCV.

Publication metadata

Author(s): South LF, Oates CJ, Mira A, Drovandi C

Publication type: Article

Publication status: Published

Journal: Bayesian Analysis

Year: 2023

Volume: 18

Issue: 3

Pages: 865-888

Online publication date: 05/09/2023

Acceptance date: 02/04/2018

Date deposited: 18/09/2023

ISSN (print): 1936-0975

ISSN (electronic): 1931-6690

Publisher: International Society for Bayesian Analysis

URL: https://doi.org/10.1214/22-BA1328

DOI: 10.1214/22-BA1328

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