Debiasing Piecewise Deterministic Markov Process samplers using couplings

TL;DR

This paper extends coupled MCMC estimators to continuous-time PDMP samplers, enabling unbiased, parallelizable estimation methods with promising scalability in high dimensions.

Contribution

It introduces couplings for PDMP samplers, adapting coupled estimators to continuous-time processes, and demonstrates their potential for unbiased, parallel computation.

Findings

Couplings developed for bouncy, boomerang, and coordinate samplers.

Preliminary results show good scaling with dimension.

Method enables unbiased, parallelizable estimation in continuous-time samplers.

Abstract

Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in alternatives to this asymptotic regime, in particular in constructing estimators that are exact in the limit of an infinite amount of computing processors, rather than in the limit of an infinite number of Markov iterations. In particular, Jacob et al. (2020) introduced coupled MCMC estimators to remove the non-asymptotic bias, resulting in MCMC estimators that can be embarrassingly parallelised. In this work, we extend the estimators of Jacob et al. (2020) to the continuous-time context and derive couplings for the bouncy, the boomerang and the coordinate samplers. Some preliminary empirical results are included that demonstrate the reasonable scaling of our method with the dimension of the target.