Irreversible Samplers from Jump and Continuous Markov Processes

TL;DR

This paper introduces irreversible variants of popular Markov Chain Monte Carlo methods, demonstrating how irreversibility can improve sampling efficiency through simple modifications and extensions.

Contribution

It presents a straightforward way to make MH and MALA algorithms irreversible, enhancing their efficiency with minimal implementation changes.

Findings

Irreversible jump sampler (I-Jump) improves sampling efficiency.

Extensions of MALA leverage irreversibility for better performance.

Experimental results show increased efficiency in various scenarios.

Abstract

In this paper, we propose irreversible versions of the Metropolis Hastings (MH) and Metropolis adjusted Langevin algorithm (MALA) with a main focus on the latter. For the former, we show how one can simply switch between different proposal and acceptance distributions upon rejection to obtain an irreversible jump sampler (I-Jump). The resulting algorithm has a simple implementation akin to MH, but with the demonstrated benefits of irreversibility. We then show how the previously proposed MALA method can also be extended to exploit irreversible stochastic dynamics as proposal distributions in the I-Jump sampler. Our experiments explore how irreversibility can increase the efficiency of the samplers in different situations.