Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911928133091328 |
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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 |