A Markov Jump Process for More Efficient Hamiltonian Monte Carlo
Machine Learning
2015-10-13 v3 Computation
Abstract
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a Hamiltonian Monte Carlo algorithm using a continuous time Markov jump process, and are thus able to escape this constraint. Transition rates in a Markov jump process need only be non-negative. We demonstrate that the new algorithm leads to improved mixing for several example problems, both by evaluating the spectral gap of the Markov operator, and by computing autocorrelation as a function of compute time. We release the algorithm as an open source Python package.
Cite
@article{arxiv.1509.03808,
title = {A Markov Jump Process for More Efficient Hamiltonian Monte Carlo},
author = {Andrew B. Berger and Mayur Mudigonda and Michael R. DeWeese and Jascha Sohl-Dickstein},
journal= {arXiv preprint arXiv:1509.03808},
year = {2015}
}