Transport Map Accelerated Markov Chain Monte Carlo
We introduce a new framework for efficient sampling from complex probability distributions, using a combination of transport maps and the Metropolis-Hastings rule. The core idea is to use deterministic couplings to transform typical Metropolis proposal mechanisms (e.g., random walks, Langevin method...
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| Format: | Article |
| Language: | English |
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Society for Industrial & Applied Mathematics (SIAM)
2020
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| Online Access: | https://hdl.handle.net/1721.1/126469 |
| _version_ | 1826206360422842368 |
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| author | Marzouk, Youssef M |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Marzouk, Youssef M |
| author_sort | Marzouk, Youssef M |
| collection | MIT |
| description | We introduce a new framework for efficient sampling from complex probability distributions, using a combination of transport maps and the Metropolis-Hastings rule. The core idea is to use deterministic couplings to transform typical Metropolis proposal mechanisms (e.g., random walks, Langevin methods) into non-Gaussian proposal distributions that can more effectively explore the target density. Our approach adaptively constructs a lower triangular transport map-an approximation of the Knothe-Rosenblatt rearrangement-using information from previous Markov chain Monte Carlo (MCMC) states, via the solution of an optimization problem. This optimization problem is convex regardless of the form of the target distribution and can be solved efficiently without gradient information from the target probability distribution; the target distribution is instead represented via samples. Sequential updates enable efficient and parallelizable adaptation of the map even for large numbers of samples. We show that this approach uses inexact or truncated maps to produce an adaptive MCMC algorithm that is ergodic for the exact target distribution. Numerical demonstrations on a range of parameter inference problems show order-of-magnitude speedups over standard MCMC techniques, measured by the number of effectively independent samples produced per target density evaluation and per unit of wallclock time. |
| first_indexed | 2024-09-23T13:28:15Z |
| format | Article |
| id | mit-1721.1/126469 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:28:15Z |
| publishDate | 2020 |
| publisher | Society for Industrial & Applied Mathematics (SIAM) |
| record_format | dspace |
| spelling | mit-1721.1/1264692022-09-28T14:30:04Z Transport Map Accelerated Markov Chain Monte Carlo Marzouk, Youssef M Massachusetts Institute of Technology. Department of Aeronautics and Astronautics We introduce a new framework for efficient sampling from complex probability distributions, using a combination of transport maps and the Metropolis-Hastings rule. The core idea is to use deterministic couplings to transform typical Metropolis proposal mechanisms (e.g., random walks, Langevin methods) into non-Gaussian proposal distributions that can more effectively explore the target density. Our approach adaptively constructs a lower triangular transport map-an approximation of the Knothe-Rosenblatt rearrangement-using information from previous Markov chain Monte Carlo (MCMC) states, via the solution of an optimization problem. This optimization problem is convex regardless of the form of the target distribution and can be solved efficiently without gradient information from the target probability distribution; the target distribution is instead represented via samples. Sequential updates enable efficient and parallelizable adaptation of the map even for large numbers of samples. We show that this approach uses inexact or truncated maps to produce an adaptive MCMC algorithm that is ergodic for the exact target distribution. Numerical demonstrations on a range of parameter inference problems show order-of-magnitude speedups over standard MCMC techniques, measured by the number of effectively independent samples produced per target density evaluation and per unit of wallclock time. United States. Department of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0009297) 2020-08-05T15:06:40Z 2020-08-05T15:06:40Z 2018-05 2017-06 2019-10-29T18:34:17Z Article http://purl.org/eprint/type/JournalArticle 2166-2525 https://hdl.handle.net/1721.1/126469 Parno, Matthew D. and Youssef Marzouk. “Transport Map Accelerated Markov Chain Monte Carlo.” SIAM/ASA journal on uncertainty quantification, vol. 6, no. 2, 2018, pp. 645-682 © 2018 The Author(s) en 10.1137/17M1134640 SIAM/ASA journal on uncertainty quantification Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial & Applied Mathematics (SIAM) SIAM |
| spellingShingle | Marzouk, Youssef M Transport Map Accelerated Markov Chain Monte Carlo |
| title | Transport Map Accelerated Markov Chain Monte Carlo |
| title_full | Transport Map Accelerated Markov Chain Monte Carlo |
| title_fullStr | Transport Map Accelerated Markov Chain Monte Carlo |
| title_full_unstemmed | Transport Map Accelerated Markov Chain Monte Carlo |
| title_short | Transport Map Accelerated Markov Chain Monte Carlo |
| title_sort | transport map accelerated markov chain monte carlo |
| url | https://hdl.handle.net/1721.1/126469 |
| work_keys_str_mv | AT marzoukyoussefm transportmapacceleratedmarkovchainmontecarlo |