Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics
Abstract 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 accelerati...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer US
2022
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| Online Access: | https://hdl.handle.net/1721.1/145563 |
| _version_ | 1811071657643606016 |
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| author | Zhang, Benjamin J. Marzouk, Youssef M. Spiliopoulos, Konstantinos |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Zhang, Benjamin J. Marzouk, Youssef M. Spiliopoulos, Konstantinos |
| author_sort | Zhang, Benjamin J. |
| collection | MIT |
| description | Abstract
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. |
| first_indexed | 2024-09-23T08:54:41Z |
| format | Article |
| id | mit-1721.1/145563 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:54:41Z |
| publishDate | 2022 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1455632023-06-28T18:52:07Z Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics Zhang, Benjamin J. Marzouk, Youssef M. Spiliopoulos, Konstantinos Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Massachusetts Institute of Technology. Center for Computational Science and Engineering Abstract 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. 2022-09-26T13:42:14Z 2022-09-26T13:42:14Z 2022-09-19 2022-09-26T12:31:41Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145563 Statistics and Computing. 2022 Sep 19;32(5):78 PUBLISHER_CC en https://doi.org/10.1007/s11222-022-10147-6 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer US Springer US |
| spellingShingle | 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 |
| url | https://hdl.handle.net/1721.1/145563 |
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