Pseudo-extended Markov chain Monte Carlo

TL;DR

This paper introduces the pseudo-extended MCMC method, which enhances sampling efficiency for multi-modal posteriors by connecting modes in an augmented state space, leading to better mixing and exploration.

Contribution

The paper proposes a novel pseudo-extended MCMC technique that augments the state space with pseudo-samples to improve mixing across modes in multi-modal distributions.

Findings

Improved mixing over Hamiltonian Monte Carlo on multi-modal posteriors

Effective in models with sparsity-inducing priors

Demonstrated on Boltzmann machines

Abstract

Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC method as a simple approach for improving the mixing of the MCMC sampler for multi-modal posterior distributions. The pseudo-extended method augments the state-space of the posterior using pseudo-samples as auxiliary variables. On the extended space, the modes of the posterior are connected, which allows the MCMC sampler to easily move between well-separated posterior modes. We demonstrate that the pseudo-extended approach delivers improved MCMC sampling over the Hamiltonian Monte Carlo algorithm on multi-modal posteriors, including Boltzmann machines and models with sparsity-inducing priors.