AutoStep: Locally adaptive involutive MCMC
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908372603764736 |
|---|---|
| author | Liu, Tiange Surjanovic, Nikola Biron-Lattes, Miguel Bouchard-Côté, Alexandre Campbell, Trevor |
| author_facet | Liu, Tiange Surjanovic, Nikola Biron-Lattes, Miguel Bouchard-Côté, Alexandre Campbell, Trevor |
| contents | 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 under mild conditions AutoStep MCMC is $π$-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and efficacy of our proposed step size selection procedure, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | AutoStep: Locally adaptive involutive MCMC Liu, Tiange Surjanovic, Nikola Biron-Lattes, Miguel Bouchard-Côté, Alexandre Campbell, Trevor Computation Machine Learning 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 under mild conditions AutoStep MCMC is $π$-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and efficacy of our proposed step size selection procedure, 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. |
| title | AutoStep: Locally adaptive involutive MCMC |
| topic | Computation Machine Learning |
| url | https://arxiv.org/abs/2410.18929 |