Fast Markov Chain Monte Carlo Algorithms via Lie Groups

2019/01/24 by Steve Huntsman, Huntsman, Steve
Computer Science · Mathematics · Physics and Astronomy · #65C05 #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Markov Chains and Monte Carlo Methods #Rings and Algebras (math.RA) #Statistics Theory (math.ST) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1901.08606

openalex publication_date 2019/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• MCMC Using Ensembles of States for Problems with Fast and Slow Variables\n such as Gaussian Process Regression
• On the stochastic Lie algebra
• Automorphism Groups of Graphical Models and Lifted Variational Inference

Related

• Accelerating MCMC Algorithms
• A Common Derivation for Markov Chain Monte Carlo Algorithms with Tractable and Intractable Targets
• Does waste-recycling really improve Metropolis-Hastings Monte Carlo algorithm?
• Fast Langevin based algorithm for MCMC in high dimensions
• Locally weighted Markov chain Monte Carlo