Metropolis Augmented Hamiltonian Monte Carlo

TL;DR

This paper introduces MAHMC, a novel HMC variant that integrates Metropolis-Hastings updates within HMC, overcoming the traditional trade-offs and improving sampling efficiency for complex distributions.

Contribution

We propose MAHMC, a new method that combines HMC with MH updates directly, eliminating the need for within-Gibbs strategies and enhancing sampling performance.

Findings

MAHMC outperforms within-Gibbs HMC in efficiency.

MAHMC is easier to implement and tune.

Experiments confirm improved sampling quality.

Abstract

Hamiltonian Monte Carlo (HMC) is a powerful Markov Chain Monte Carlo (MCMC) method for sampling from complex high-dimensional continuous distributions. However, in many situations it is necessary or desirable to combine HMC with other Metropolis-Hastings (MH) samplers. The common HMC-within-Gibbs strategy implies a trade-off between long HMC trajectories and more frequent other MH updates. Addressing this trade-off has been the focus of several recent works. In this paper we propose Metropolis Augmented Hamiltonian Monte Carlo (MAHMC), an HMC variant that allows MH updates within HMC and eliminates this trade-off. Experiments on two representative examples demonstrate MAHMC's efficiency and ease of use when compared with within-Gibbs alternatives.