A piecewise deterministic scaling limit of Lifted Metropolis-Hastings in the Curie-Weiss model

Abstract

In Turitsyn, Chertkov, Vucelja (2011) a non-reversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis-Hastings (LMH). A scaling limit of the magnetization process in the Curie-Weiss model is derived for LMH, as well as for Metropolis-Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals $n^{1/2}$ for LMH, which should be compared to $n$ for MH. At the critical temperature the required jump rate equals $n^{3/4}$ for LMH and $n^{3/2}$ for MH, in agreement with experimental results of Turitsyn, Chertkov, Vucelja (2011). The scaling limit of LMH turns out to be a non-reversible piecewise deterministic exponentially ergodic `zig-zag' Markov process.

References in corpus (4)

• Variance Reduction using Nonreversible Langevin Samplers
• Irreversible Langevin samplers and variance reduction: a large deviation approach
• The mixing time evolution of Glauber dynamics for the mean-field Ising model
• Improving the Asymptotic Performance of Markov Chain Monte-Carlo by Inserting Vortices

Cited by in corpus (19)

• The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data
• Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo
• Ergodicity of the zigzag process
• Event-chain Monte Carlo: foundations, applications, and prospects
• Piecewise Deterministic Markov Processes for Scalable Monte Carlo on Restricted Domains
• Limit theorems for the Zig-Zag process
• Bayesian Mechanics for Stationary Processes
• Large deviations for the Skew-Detailed-Balance Lifted-Markov processes to sample the equilibrium distribution of the Curie-Weiss model
• Irreversible Samplers from Jump and Continuous Markov Processes
• Zig-zag sampling for discrete structures and non-reversible phylogenetic MCMC
• Direction-sweep Markov chains
• Non-reversible lifts of reversible diffusion processes and relaxation times
• Complexity of zigzag sampling algorithm for strongly log-concave distributions
• Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models
• Symmetry breaking at a topological phase transition
• On the asymptotic variance of reversible Markov chain without cycles
• Super-Efficient Exact Hamiltonian Monte Carlo for the von Mises Distribution
• Emergent electrostatics in planar XY spin models: the bridge connecting topological order with broken $U(1)$ symmetry
• Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs