AutoStep: Locally adaptive involutive MCMC

• URL: http://arxiv.org/abs/2410.18929v1
• Date: Thu, 24 Oct 2024 17:17:11 GMT
• Title: AutoStep: Locally adaptive involutive MCMC
• Authors: Tiange Liu, Nikola Surjanovic, Miguel Biron-Lattes, Alexandre Bouchard-Côté, Trevor Campbell,
• Abstract summary: AutoStep MCMC selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost.
• Score: 51.186543293659376
• License:
• Abstract: Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods -- AutoStep MCMC -- that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that AutoStep MCMC is $\pi$-invariant and has other desirable properties under mild assumptions on the target distribution $\pi$ and involutive proposal. Empirical results examine the effect of various step size selection design choices, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

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