Convergence Rates for the Constrained Sampling via Langevin Monte Carlo

Autor:	Yuanzheng Zhu
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Bayesian computation constrained sampling convex support Langevin Monte Carlo MCMC mixing time bound Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 25, Iss 8, p 1234 (2023)
Druh dokumentu:	article
ISSN:	1099-4300
DOI:	10.3390/e25081234
Popis:	Sampling from constrained distributions has posed significant challenges in terms of algorithmic design and non-asymptotic analysis, which are frequently encountered in statistical and machine-learning models. In this study, we propose three sampling algorithms based on Langevin Monte Carlo with the Metropolis–Hastings steps to handle the distribution constrained within some convex body. We present a rigorous analysis of the corresponding Markov chains and derive non-asymptotic upper bounds on the convergence rates of these algorithms in total variation distance. Our results demonstrate that the sampling algorithm, enhanced with the Metropolis–Hastings steps, offers an effective solution for tackling some constrained sampling problems. The numerical experiments are conducted to compare our methods with several competing algorithms without the Metropolis–Hastings steps, and the results further support our theoretical findings.
Databáze:	Directory of Open Access Journals
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