 Smoothing unadjusted Langevin algorithms for nonsmooth composite potential functionsSusan Ghaderi, Masoud Ahookhosh, Adam Arany, Alexander Skupin, Panagiotis Patrinos and Yves Moreau Applied Mathematics and Computation, 2024, vol. 464, issue C Abstract: This paper addresses a gradient-based Markov Chain Monte Carlo (MCMC) method to sample from the posterior distribution of problems with nonsmooth potential functions. Following the Bayesian paradigm, our potential function will be some of two convex functions, where one of which is smooth. We first approximate the potential function by the so-called forward-backward envelope function, which is a real-valued smooth function with the same critical points as the original one. Then, we incorporate this smoothing technique with the unadjusted Langevin algorithm (ULA), leading to smoothing ULA, called SULA. We next establish non-asymptotic convergence results of SULA under mild assumption on the original potential function. We finally report some numerical results to establish the promising performance of SULA on both synthetic and real chemoinformatics data. Keywords: Bayesian learning; Nonsmooth sampling; Convex optimization; MCMC methods; Langevin equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:464:y:2024:i:c:s0096300323005465 DOI: 10.1016/j.amc.2023.128377 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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