Fast Markov Chain Monte Carlo Algorithms via Lie Groups
Statistics Theory
2020-01-29 v2 Group Theory
Rings and Algebras
Computation
Statistics Theory
Abstract
From basic considerations of the Lie group that preserves a target probability measure, we derive the Barker, Metropolis, and ensemble Markov chain Monte Carlo (MCMC) algorithms, as well as variants of waste-recycling Metropolis-Hastings and an altogether new MCMC algorithm. We illustrate these constructions with explicit numerical computations, and we empirically demonstrate on a spin glass that the new algorithm converges more quickly than its siblings.
Cite
@article{arxiv.1901.08606,
title = {Fast Markov Chain Monte Carlo Algorithms via Lie Groups},
author = {Steve Huntsman},
journal= {arXiv preprint arXiv:1901.08606},
year = {2020}
}
Comments
Accepted to AISTATS 2020; proofs included here as an appendix (but relegated to supplementary info in conference version)