Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime

Fuente: arXiv
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Main Authors: Bou-Rabee, Nawaf, Oberdörster, Stefan
Format: Preprint
Published: 2023
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author Bou-Rabee, Nawaf
Oberdörster, Stefan
author_facet Bou-Rabee, Nawaf
Oberdörster, Stefan
contents We present a coupling framework to upper bound the total variation mixing time of various Metropolis-adjusted, gradient-based Markov kernels in the `high acceptance regime'. The approach uses a localization argument to boost local mixing of the underlying unadjusted kernel to mixing of the adjusted kernel when the acceptance rate is suitably high. As an application, mixing time guarantees are developed for a non-reversible, adjusted Markov chain based on the kinetic Langevin diffusion, where little is currently understood.
format Preprint
id arxiv_https___arxiv_org_abs_2308_04634
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime
Bou-Rabee, Nawaf
Oberdörster, Stefan
Probability
60J05
We present a coupling framework to upper bound the total variation mixing time of various Metropolis-adjusted, gradient-based Markov kernels in the `high acceptance regime'. The approach uses a localization argument to boost local mixing of the underlying unadjusted kernel to mixing of the adjusted kernel when the acceptance rate is suitably high. As an application, mixing time guarantees are developed for a non-reversible, adjusted Markov chain based on the kinetic Langevin diffusion, where little is currently understood.
title Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime
topic Probability
60J05
url https://arxiv.org/abs/2308.04634