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arXiv · 1509.03808

A Markov Jump Process for More Efficient Hamiltonian Monte Carlo

Andrew B. Berger·Mayur Mudigonda·Michael R. DeWeese·Jascha Sohl-Dickstein
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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.

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Andrew B. Berger, Mayur Mudigonda, Michael R. DeWeese, Jascha Sohl-Dickstein. 2015-09-13. A Markov Jump Process for More Efficient Hamiltonian Monte Carlo. https://arxiv.org/abs/1509.03808

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