Theoretical guarantees for neural control variates in MCMC
Statistics Theory
2024-10-29 v2 Machine Learning
Probability
Methodology
Machine Learning
Statistics Theory
Abstract
In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates are represented as deep neural networks. We derive the optimal convergence rate of the asymptotic variance under various ergodicity assumptions on the underlying Markov chain. The proposed approach relies upon recent results on the stochastic errors of variance reduction algorithms and function approximation theory.
Cite
@article{arxiv.2304.01111,
title = {Theoretical guarantees for neural control variates in MCMC},
author = {Denis Belomestny and Artur Goldman and Alexey Naumov and Sergey Samsonov},
journal= {arXiv preprint arXiv:2304.01111},
year = {2024}
}