Unbiased Hamiltonian Monte Carlo with couplings

TL;DR

This paper introduces a novel method for parallelizing Hamiltonian Monte Carlo by coupling chains to achieve unbiased estimators, enabling efficient and scalable Bayesian inference in high-dimensional models.

Contribution

It presents a new coupling technique for Hamiltonian Monte Carlo that produces unbiased estimators and allows parallel computation of independent replicates.

Findings

Coupling method achieves unbiased estimators in HMC.

Method scales effectively to high-dimensional problems.

Demonstrated on logistic regression and Cox process models.

Abstract

We propose a methodology to parallelize Hamiltonian Monte Carlo estimators. Our approach constructs a pair of Hamiltonian Monte Carlo chains that are coupled in such a way that they meet exactly after some random number of iterations. These chains can then be combined so that resulting estimators are unbiased. This allows us to produce independent replicates in parallel and average them to obtain estimators that are consistent in the limit of the number of replicates, instead of the usual limit of the number of Markov chain iterations. We investigate the scalability of our coupling in high dimensions on a toy example. The choice of algorithmic parameters and the efficiency of our proposed methodology are then illustrated on a logistic regression with 300 covariates, and a log-Gaussian Cox point processes model with low to fine grained discretizations.