Enhanced gradient-based MCMC in discrete spaces

Published: 13 Oct 2022, Last Modified: 28 Feb 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: The recent introduction of gradient-based Markov chain Monte Carlo (MCMC) for discrete spaces holds great promise, and comes with the tantalising possibility of new discrete counterparts to celebrated continuous methods such as the Metropolis-adjusted Langevin algorithm (MALA). Towards this goal, we introduce several discrete Metropolis-Hastings samplers that are conceptually inspired by MALA, and demonstrate their strong empirical performance across a range of challenging sampling problems in Bayesian inference and energy-based modelling. Methodologically, we identify why discrete analogues to \emph{preconditioned} MALA are generally intractable, motivating us to introduce a new kind of preconditioning based on auxiliary variables and the `Gaussian integral trick'.
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Roman_Garnett1
Submission Number: 359