Involutive MCMC: a Unifying Framework

TL;DR

This paper introduces Involutive MCMC (iMCMC), a unifying framework that consolidates various MCMC algorithms, enabling the development of more efficient irreversible methods and offering new design principles.

Contribution

The paper unifies diverse MCMC algorithms under the iMCMC framework and provides strategies for creating improved irreversible sampling methods.

Findings

Unified view of many MCMC algorithms

Transformation of reversible to irreversible MCMC methods

Enhanced efficiency of sampling algorithms

Abstract

Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated, the way they are applied and how efficiently they sample. Despite all the differences, many of them share the same core principle, which we unify as the Involutive MCMC (iMCMC) framework. Building upon this, we describe a wide range of MCMC algorithms in terms of iMCMC, and formulate a number of "tricks" which one can use as design principles for developing new MCMC algorithms. Thus, iMCMC provides a unified view of many known MCMC algorithms, which facilitates the derivation of powerful extensions. We demonstrate the latter with two examples where we transform known reversible MCMC algorithms into more efficient irreversible ones.