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.


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.

Related Material