Fast Markov chain Monte Carlo algorithms via Lie groups

Steve Huntsman
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2841-2851, 2020.

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 this Paper


BibTeX
@InProceedings{pmlr-v108-huntsman20a, title = {Fast Markov chain Monte Carlo algorithms via Lie groups}, author = {Huntsman, Steve}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2841--2851}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/huntsman20a/huntsman20a.pdf}, url = { http://proceedings.mlr.press/v108/huntsman20a.html }, 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.} }
Endnote
%0 Conference Paper %T Fast Markov chain Monte Carlo algorithms via Lie groups %A Steve Huntsman %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-huntsman20a %I PMLR %P 2841--2851 %U http://proceedings.mlr.press/v108/huntsman20a.html %V 108 %X 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.
APA
Huntsman, S.. (2020). Fast Markov chain Monte Carlo algorithms via Lie groups. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2841-2851 Available from http://proceedings.mlr.press/v108/huntsman20a.html .

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