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arXiv · 2302.01378

Optimal Ricci curvature Markov chain Monte Carlo methods on finite states

Wuchen Li·Linyuan Lu
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Abstract

We construct a new Markov chain Monte Carlo method on finite states with optimal choices of acceptance-rejection ratio functions. We prove that the constructed continuous time Markov jumping process has a global in-time convergence rate in $L^1$ distance. The convergence rate is no less than one-half and is independent of the target distribution. For example, our method recovers the Metropolis-Hastings algorithm on a two-point state. And it forms a new algorithm for sampling general target distributions. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

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Wuchen Li, Linyuan Lu. 2023-02-02. Optimal Ricci curvature Markov chain Monte Carlo methods on finite states. https://arxiv.org/abs/2302.01378

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