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 · Wed Dec 13 00:00:00 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:: ARC Centre of Excellence; USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 2281802

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

A tutorial on adaptive MCMC Andrieu, Christophe; Thoms, Johannes Statistics and Computing, Vol. 18, Issue 4 https://doi.org/10.1007/s11222-008-9110-y	journal	December 2008
Sampling using a ‘bank’ of clues Allanach, Benjamin C.; Lester, Christopher G. Computer Physics Communications, Vol. 179, Issue 4 https://doi.org/10.1016/j.cpc.2008.02.020	journal	August 2008
Equation of State Calculations by Fast Computing Machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. The Journal of Chemical Physics, Vol. 21, Issue 6 https://doi.org/10.1063/1.1699114	journal	June 1953
Adaptive Monte Carlo augmented with normalizing flows Gabrié, Marylou; Rotskoff, Grant M.; Vanden-Eijnden, Eric Proceedings of the National Academy of Sciences, Vol. 119, Issue 10 https://doi.org/10.1073/pnas.2109420119	journal	March 2022
`emcee` : The MCMC Hammer Foreman-Mackey, Daniel; Hogg, David W.; Lang, Dustin Publications of the Astronomical Society of the Pacific, Vol. 125, Issue 925 https://doi.org/10.1086/670067	journal	March 2013
Monte Carlo sampling methods using Markov chains and their applications Hastings, W. K. Biometrika, Vol. 57, Issue 1 https://doi.org/10.1093/biomet/57.1.97	journal	April 1970
Flow-based generative models for Markov chain Monte Carlo in lattice field theory Albergo, M. S.; Kanwar, G.; Shanahan, P. E. Physical Review D, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevD.100.034515	journal	August 2019
Sampling using SU ( N ) gauge equivariant flows Boyda, Denis; Kanwar, Gurtej; Racanière, Sébastien Physical Review D, Vol. 103, Issue 7 https://doi.org/10.1103/PhysRevD.103.074504	journal	April 2021
Determination of uncertainties in parton densities Hunt-Smith, N. T.; Accardi, A.; Melnitchouk, W. Physical Review D, Vol. 106, Issue 3 https://doi.org/10.1103/PhysRevD.106.036003	journal	August 2022
Collider constraints on electroweakinos in the presence of a light gravitino Ananyev, Viktor; Balázs, Csaba; Beniwal, Ankit The European Physical Journal C, Vol. 83, Issue 6 https://doi.org/10.1140/epjc/s10052-023-11574-z	journal	June 2023

Similar Records

A Markov-Chain Monte-Carlo Based Method for Flaw Detection in Beams

Journal Article · Thu Sep 28 00:00:00 EDT 2006 · Journal of Engineering Mechanics, vol. 133, no. 12, December 1, 2007, pp. 1258-1267 · OSTI ID:936952

Bayesian calibration of terrestrial ecosystem models: A study of advanced Markov chain Monte Carlo methods

Journal Article · Tue Feb 21 19:00:00 EST 2017 · Biogeosciences Discussions (Online) · OSTI ID:1365814

Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling

Journal Article · Mon Dec 31 23:00:00 EST 2007 · International Journal of Nonlinear Sciences and Numerical Simulation · OSTI ID:960766

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Markov Chain Monte Carlo
diffusion model
machine learning
statistical methods

Accelerating Markov Chain Monte Carlo sampling with diffusion models

Citation Formats

References (10)

Similar Records

Related Subjects