Efficient Irreversible Monte Carlo samplers

TL;DR

This paper introduces two novel irreversible Markov chain Monte Carlo algorithms for discrete systems, demonstrating significant improvements in mixing times and autocorrelation properties in the 1D 4-state Potts model.

Contribution

The paper develops two new irreversible MCMC algorithms based on the lifting framework with skewed detailed balance, applicable to general discrete spin systems.

Findings

Reduced autocorrelation times for magnetisation and energy density.

Lowered dynamical scaling exponent from ~1 to ~0.5.

Square root reduction in mixing time at high temperatures.

Abstract

We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems, one of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the Metropolized-Gibbs sampler. The algorithms we present incorporate the lifting framework with skewed detailed balance condition and construct irreversible Markov chains that satisfy the balance condition. We have applied our algorithms to 1D 4-state Potts model. The integrated autocorrelation times for magnetisation and energy density indicate a reduction of the dynamical scaling exponent from $z \approx 1$ to $z \approx 1/2$. In addition, we have generalized an irreversible Metropolis-Hastings algorithm with skewed detailed balance, initially introduced by Turitsyn et al. (2011) for the mean field Ising model, to be now readily applicable to classical spin systems in general; application to 1D 4-state Potts model indicate a square root reduction of the mixing time at high temperatures.