Accelerating Markov Chain Monte Carlo sampling with diffusion models

Hunt-Smith, Nicholas T.; Melnitchouk, Wally; Ringer, Felix; Sato, Nobuo; Thomas, Anthony W.; White, Martin J.

doi:10.1016/j.cpc.2023.109059

Accelerating Markov Chain Monte Carlo sampling with diffusion models

Journal Article · Tue Dec 12 23:00:00 EST 2023 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2023.109059· OSTI ID:2281802

^[1]; Melnitchouk, Wally ^[2]; Ringer, Felix ^[3]; Sato, Nobuo ^[2]; Thomas, Anthony W. ^[1]; White, Martin J. ^[1]

Univ. of Adelaide, SA (Australia). CSSM and ARC Centre of Excellence for Dark Matter Particle Physics
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States)

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global fit of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalising flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.

Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); ARC Centre of Excellence

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 2281802

Report Number(s):: JLAB-THY--23-3900; DOE/OR/23177-7034; CE200100008

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Vol. 296; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (10)

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