Non-reversible parallel tempering: a scalable highly parallel MCMC scheme
Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of N interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Wiley
2021
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| _version_ | 1826309018819231744 |
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| author | Syed, S Bouchard-Cote, A Deligiannidis, G Doucet, A |
| author_facet | Syed, S Bouchard-Cote, A Deligiannidis, G Doucet, A |
| author_sort | Syed, S |
| collection | OXFORD |
| description | Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of N interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and performance of reversible versus non-reversible PT schemes. We show theoretically and empirically that a class of non-reversible PT methods dominates its reversible counterparts and identify distinct scaling limits for the non-reversible and reversible schemes, the former being a piecewise-deterministic Markov process and the latter a diffusion. These results are exploited to identify the optimal annealing schedule for non-reversible PT and to develop an iterative scheme approximating this schedule. We provide a wide range of numerical examples supporting our theoretical and methodological contributions. The proposed methodology is applicable to sample from a distribution π with a density L with respect to a reference distribution (Formula presented.) and compute the normalizing constant (Formula presented.). A typical use case is when (Formula presented.) is a prior distribution, L a likelihood function and π the corresponding posterior distribution. |
| first_indexed | 2024-03-07T07:27:58Z |
| format | Journal article |
| id | oxford-uuid:d26dd57a-cba6-4e6d-b3d2-c2dc8932055f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:27:58Z |
| publishDate | 2021 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:d26dd57a-cba6-4e6d-b3d2-c2dc8932055f2022-12-05T08:58:44ZNon-reversible parallel tempering: a scalable highly parallel MCMC schemeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d26dd57a-cba6-4e6d-b3d2-c2dc8932055fEnglishSymplectic ElementsWiley2021Syed, SBouchard-Cote, ADeligiannidis, GDoucet, AParallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of N interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and performance of reversible versus non-reversible PT schemes. We show theoretically and empirically that a class of non-reversible PT methods dominates its reversible counterparts and identify distinct scaling limits for the non-reversible and reversible schemes, the former being a piecewise-deterministic Markov process and the latter a diffusion. These results are exploited to identify the optimal annealing schedule for non-reversible PT and to develop an iterative scheme approximating this schedule. We provide a wide range of numerical examples supporting our theoretical and methodological contributions. The proposed methodology is applicable to sample from a distribution π with a density L with respect to a reference distribution (Formula presented.) and compute the normalizing constant (Formula presented.). A typical use case is when (Formula presented.) is a prior distribution, L a likelihood function and π the corresponding posterior distribution. |
| spellingShingle | Syed, S Bouchard-Cote, A Deligiannidis, G Doucet, A Non-reversible parallel tempering: a scalable highly parallel MCMC scheme |
| title | Non-reversible parallel tempering: a scalable highly parallel MCMC scheme |
| title_full | Non-reversible parallel tempering: a scalable highly parallel MCMC scheme |
| title_fullStr | Non-reversible parallel tempering: a scalable highly parallel MCMC scheme |
| title_full_unstemmed | Non-reversible parallel tempering: a scalable highly parallel MCMC scheme |
| title_short | Non-reversible parallel tempering: a scalable highly parallel MCMC scheme |
| title_sort | non reversible parallel tempering a scalable highly parallel mcmc scheme |
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