Variable length trajectory compressible hybrid Monte Carlo

TL;DR

This paper introduces a flexible extension to compressible hybrid Monte Carlo that allows variable trajectory lengths and improves efficiency by reducing computation waste, broadening the applicability of HMC methods.

Contribution

It presents a generalized framework for CHMC that permits variable integration times and enhances efficiency through reduced rejected proposals.

Findings

Enables variable trajectory lengths in CHMC.

Improves sampling efficiency by reducing rejected proposals.

Demonstrates effectiveness with unstable numerical approximations.

Abstract

Hybrid Monte Carlo (HMC) generates samples from a prescribed probability distribution in a configuration space by simulating Hamiltonian dynamics, followed by the Metropolis (-Hastings) acceptance/rejection step. Compressible HMC (CHMC) generalizes HMC to a situation in which the dynamics is reversible but not necessarily Hamiltonian. This article presents a framework to further extend the algorithm. Within the existing framework, each trajectory of the dynamics must be integrated for the same amount of (random) time to generate a valid Metropolis proposal. Our generalized acceptance/rejection mechanism allows a more deliberate choice of the integration time for each trajectory. The proposed algorithm in particular enables an effective application of variable step size integrators to HMC-type sampling algorithms based on reversible dynamics. The potential of our framework is further demonstrated by another extension of HMC which reduces the wasted computations due to unstable numerical approximations and corresponding rejected proposals.