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Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics
We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation. It is well documented that there exist perturbations to the Langevin dynamics that preserve its invariant measure while accelerating its convergence. Irre...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9485103/ https://www.ncbi.nlm.nih.gov/pubmed/36156938 http://dx.doi.org/10.1007/s11222-022-10147-6 |
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author | Zhang, Benjamin J. Marzouk, Youssef M. Spiliopoulos, Konstantinos |
author_facet | Zhang, Benjamin J. Marzouk, Youssef M. Spiliopoulos, Konstantinos |
author_sort | Zhang, Benjamin J. |
collection | PubMed |
description | We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation. It is well documented that there exist perturbations to the Langevin dynamics that preserve its invariant measure while accelerating its convergence. Irreversible perturbations and reversible perturbations (such as Riemannian manifold Langevin dynamics (RMLD)) have separately been shown to improve the performance of Langevin samplers. We consider these two perturbations simultaneously by presenting a novel form of irreversible perturbation for RMLD that is informed by the underlying geometry. Through numerical examples, we show that this new irreversible perturbation can improve estimation performance over irreversible perturbations that do not take the geometry into account. Moreover we demonstrate that irreversible perturbations generally can be implemented in conjunction with the stochastic gradient version of the Langevin algorithm. Lastly, while continuous-time irreversible perturbations cannot impair the performance of a Langevin estimator, the situation can sometimes be more complicated when discretization is considered. To this end, we describe a discrete-time example in which irreversibility increases both the bias and variance of the resulting estimator. |
format | Online Article Text |
id | pubmed-9485103 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-94851032022-09-21 Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics Zhang, Benjamin J. Marzouk, Youssef M. Spiliopoulos, Konstantinos Stat Comput Article We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation. It is well documented that there exist perturbations to the Langevin dynamics that preserve its invariant measure while accelerating its convergence. Irreversible perturbations and reversible perturbations (such as Riemannian manifold Langevin dynamics (RMLD)) have separately been shown to improve the performance of Langevin samplers. We consider these two perturbations simultaneously by presenting a novel form of irreversible perturbation for RMLD that is informed by the underlying geometry. Through numerical examples, we show that this new irreversible perturbation can improve estimation performance over irreversible perturbations that do not take the geometry into account. Moreover we demonstrate that irreversible perturbations generally can be implemented in conjunction with the stochastic gradient version of the Langevin algorithm. Lastly, while continuous-time irreversible perturbations cannot impair the performance of a Langevin estimator, the situation can sometimes be more complicated when discretization is considered. To this end, we describe a discrete-time example in which irreversibility increases both the bias and variance of the resulting estimator. Springer US 2022-09-19 2022 /pmc/articles/PMC9485103/ /pubmed/36156938 http://dx.doi.org/10.1007/s11222-022-10147-6 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Zhang, Benjamin J. Marzouk, Youssef M. Spiliopoulos, Konstantinos Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics |
title | Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics |
title_full | Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics |
title_fullStr | Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics |
title_full_unstemmed | Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics |
title_short | Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics |
title_sort | geometry-informed irreversible perturbations for accelerated convergence of langevin dynamics |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9485103/ https://www.ncbi.nlm.nih.gov/pubmed/36156938 http://dx.doi.org/10.1007/s11222-022-10147-6 |
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