Hamiltonian Monte Carlo Without Detailed Balance

TL;DR

This paper introduces a modified Hamiltonian Monte Carlo method that reduces sample rejection by using non-detailed balance Markov transitions, leading to faster mixing times and more efficient sampling.

Contribution

It proposes a novel HMC algorithm that eliminates most rejections by satisfying fixed point equations without detailed balance, improving sampling efficiency.

Findings

Over two times faster mixing on test problems

Significant reduction in rejected samples

Open-source Python and MATLAB implementations

Abstract

We present a method for performing Hamiltonian Monte Carlo that largely eliminates sample rejection for typical hyperparameters. In situations that would normally lead to rejection, instead a longer trajectory is computed until a new state is reached that can be accepted. This is achieved using Markov chain transitions that satisfy the fixed point equation, but do not satisfy detailed balance. The resulting algorithm significantly suppresses the random walk behavior and wasted function evaluations that are typically the consequence of update rejection. We demonstrate a greater than factor of two improvement in mixing time on three test problems. We release the source code as Python and MATLAB packages.