Modified Hamiltonian Monte Carlo for Bayesian Inference

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible part of the dynamics into a chain. This is achieved by replacin...

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Detalhes bibliográficos
Autores: Radivojevic, T., Akhmatskaya, E.
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2019
País:España
Recursos:Basque Center for Applied Mathematics (BCAM)
Repositório:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1001
Acesso em linha:http://hdl.handle.net/20.500.11824/1001
https://doi.org/10.1007/s11222-019-09885-x
Access Level:Acesso embargado
Palavra-chave:Bayesian inference
Markov chain Monte Carlo
Hamiltonian Monte Carlo
importance sampling
modified Hamiltonians
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spelling Modified Hamiltonian Monte Carlo for Bayesian InferenceRadivojevic, T.Akhmatskaya, E.Bayesian inferenceMarkov chain Monte CarloHamiltonian Monte Carloimportance samplingmodified HamiltoniansThe Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible part of the dynamics into a chain. This is achieved by replacing Hamiltonians in the Metropolis test with modified Hamiltonians, and a complete momentum update with a partial momentum refreshment. We call the resulting generalized HMC importance sampler—Mix & Match Hamiltonian Monte Carlo (MMHMC). The method is irreversible by construction and further benefits from (i) the efficient algorithms for computation of modified Hamiltonians; (ii) the implicit momentum update procedure and (iii) the multi-stage splitting integrators specially derived for the methods sampling with modified Hamiltonians. MMHMC has been implemented, tested on the popular statistical models and compared in sampling efficiency with HMC, Riemann Manifold Hamiltonian Monte Carlo, Generalized Hybrid Monte Carlo, Generalized Shadow Hybrid Monte Carlo, Metropolis Adjusted Langevin Algorithm and Random Walk Metropolis-Hastings. To make a fair comparison, we propose a metric that accounts for correlations among samples and weights, and can be readily used for all methods which generate such samples. The experiments reveal the superiority of MMHMC over popular sampling techniques, especially in solving high dimensional problems.Agile BioFoundry (http://agilebiofoundry.org) supported by the U.S. Department of Energy, Energy Efficiency and Renewable Energy, Bioenergy Technologies Office, through contract DE-AC02-05CH11231 between Lawrence Berkeley National Laboratory and the U.S. Department of Energy.info201920192019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1001https://doi.org/10.1007/s11222-019-09885-xreponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://doi.org/10.1007/s11222-019-09885-xinfo:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/MINECO//MTM2016-76329-Rinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/embargoedAccessoai:bird.bcamath.org:20.500.11824/10012026-06-19T12:47:47Z
dc.title.none.fl_str_mv Modified Hamiltonian Monte Carlo for Bayesian Inference
title Modified Hamiltonian Monte Carlo for Bayesian Inference
spellingShingle Modified Hamiltonian Monte Carlo for Bayesian Inference
Radivojevic, T.
Bayesian inference
Markov chain Monte Carlo
Hamiltonian Monte Carlo
importance sampling
modified Hamiltonians
title_short Modified Hamiltonian Monte Carlo for Bayesian Inference
title_full Modified Hamiltonian Monte Carlo for Bayesian Inference
title_fullStr Modified Hamiltonian Monte Carlo for Bayesian Inference
title_full_unstemmed Modified Hamiltonian Monte Carlo for Bayesian Inference
title_sort Modified Hamiltonian Monte Carlo for Bayesian Inference
dc.creator.none.fl_str_mv Radivojevic, T.
Akhmatskaya, E.
author Radivojevic, T.
author_facet Radivojevic, T.
Akhmatskaya, E.
author_role author
author2 Akhmatskaya, E.
author2_role author
dc.subject.none.fl_str_mv Bayesian inference
Markov chain Monte Carlo
Hamiltonian Monte Carlo
importance sampling
modified Hamiltonians
topic Bayesian inference
Markov chain Monte Carlo
Hamiltonian Monte Carlo
importance sampling
modified Hamiltonians
description The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible part of the dynamics into a chain. This is achieved by replacing Hamiltonians in the Metropolis test with modified Hamiltonians, and a complete momentum update with a partial momentum refreshment. We call the resulting generalized HMC importance sampler—Mix & Match Hamiltonian Monte Carlo (MMHMC). The method is irreversible by construction and further benefits from (i) the efficient algorithms for computation of modified Hamiltonians; (ii) the implicit momentum update procedure and (iii) the multi-stage splitting integrators specially derived for the methods sampling with modified Hamiltonians. MMHMC has been implemented, tested on the popular statistical models and compared in sampling efficiency with HMC, Riemann Manifold Hamiltonian Monte Carlo, Generalized Hybrid Monte Carlo, Generalized Shadow Hybrid Monte Carlo, Metropolis Adjusted Langevin Algorithm and Random Walk Metropolis-Hastings. To make a fair comparison, we propose a metric that accounts for correlations among samples and weights, and can be readily used for all methods which generate such samples. The experiments reveal the superiority of MMHMC over popular sampling techniques, especially in solving high dimensional problems.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019
2019
info
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1001
https://doi.org/10.1007/s11222-019-09885-x
url http://hdl.handle.net/20.500.11824/1001
https://doi.org/10.1007/s11222-019-09885-x
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1007/s11222-019-09885-x
info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/MINECO//MTM2016-76329-R
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/embargoedAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
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instname:Basque Center for Applied Mathematics (BCAM)
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