Bayes Reading Group: Werner Krauth [ENS]

Friday May 10, 2024, 11:00 AM → 12:00 PM America/New_York

3rd Floor Conference Room/3-Flatiron Institute (162 5th Avenue)

Discussion Lead: Werner Krauth [ENS]

Topic: Lifted Markov chains: from solvable models to applications in chemical physics.

Link: (1) Diaconis, Holmes, Neal, Analysis of a nonreversible Markov chain sampler, Ann. Appl. Probab. 10, 726 (2000).

(2) Chen, Lovacz, Pak, Lifting Markov Chains to Speed up Mixing, Proceedings of the 17th Annual ACM Symposium on Theory of Computing, 275 (1999).

(3) Essler, Krauth, Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains,” arXiv: 2306.13059 (2023).

(4) Kapfer, Krauth, Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium, Phys. Rev. Lett. 119, 240603 (2017).

(5) Bernard, Krauth, Wilson, Event-chain Monte Carlo algorithms for hard-sphere systems, Phys. Rev. E 80, 056704 (2009).

(6) Bernard, Krauth, Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition, Phys. Rev. Lett. 107, 155704 (2011).

(7) Hoellmer, Maggs, Krauth, Molecular simulation from modern statistics: Continuous-time, continuous-space, exact, arXiv: 2305.02979 (2023)

(8) Michel, Kapfer, Krauth,  Generalized event-chain Monte Carlo..., J. Chem. Phys. 140, 054116 (2014).

Abstract: I will discuss lifted Markov chains (1,2), a group of sampling methods where non-reversibility plays a crucial role. A lifted Markov chain starts from a usually reversible "collapsed" chain, with a given stationary distribution (2), whose samples are multiplied ("lifted"). Only non-reversible liftings may achieve significant speedups for convergence. I will present  solvable models (1,3,4), among them the lifted TASEP, a one-dimensional N-particle model, but also real-world applications to the hard-disk model of statistical physics (5,6) and the SPC/Fw water model of chemical physics (7). Lifted Markov chains are related to Hamiltonian Monte Carlo, but they are neither gradient-based nor time-driven. Much rather, they are rooted in the factorized Metropolis filter (8), which allows them to exactly sample the Boltzmann distribution exp(-beta U) without ever evaluating U or grad U and, in addition, without rejections.