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dc.contributor.authorHartmann, Marcelo
dc.contributor.authorGirolami, Mark
dc.contributor.authorKlami, Arto
dc.date.accessioned2022-03-02T00:30:06Z
dc.date.available2022-03-02T00:30:06Z
dc.date.issued2022
dc.identifier.issn2640-3498
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/334561
dc.description.abstractThe efficiency of Markov Chain Monte Carlo (MCMC) depends on how the underlying geometry of the problem is taken into account. For distributions with strongly varying curvature, Riemannian metrics help in efficient exploration of the target distribution. Unfortunately, they have significant computational overhead due to e.g. repeated inversion of the metric tensor, and current geometric MCMC methods using the Fisher information matrix to induce the manifold are in practice slow. We propose a new alternative Riemannian metric for MCMC, by embedding the target distribution into a higher-dimensional Euclidean space as a Monge patch and using the induced metric determined by direct geometric reasoning. Our metric only requires first-order gradient information and has fast inverse and determinants, and allows reducing the computational complexity of individual iterations from cubic to quadratic in the problem dimensionality. We demonstrate how Lagrangian Monte Carlo in this metric efficiently explores the target distributions.
dc.publisherPMLR
dc.rightsAll Rights Reserved
dc.rights.urihttp://www.rioxx.net/licenses/all-rights-reserved
dc.subjectstat.ME
dc.subjectstat.ME
dc.subjectcs.AI
dc.subjectcs.LG
dc.titleLagrangian Manifold Monte Carlo on Monge Patches
dc.typeArticle
dc.publisher.departmentDepartment of Engineering
dc.date.updated2022-02-08T17:33:32Z
prism.publicationNameINTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 151
dc.identifier.doi10.17863/CAM.81980
dcterms.dateAccepted2022-02-08
rioxxterms.versionAM
dc.contributor.orcidGirolami, Mark [0000-0003-3008-253X]
dc.publisher.urlhttp://proceedings.mlr.press/v151/
rioxxterms.typeJournal Article/Review
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/R034710/1)
pubs.funder-project-idRoyal Academy of Engineering (RAEng) (RCSRF\1718\6\34)
pubs.funder-project-idEPSRC (via University of Warwick) (EP/R034710/1)
pubs.funder-project-idEPSRC (EP/V056441/1)
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/V056522/1)
pubs.conference-nameInternational Conference on Artificial Intelligence and Statistics (AISTATS '22)
pubs.conference-start-date2022-03-28
cam.orpheus.counter26*
cam.depositDate2022-02-08
pubs.conference-finish-date2022-03-30
pubs.licence-identifierapollo-deposit-licence-2-1
pubs.licence-display-nameApollo Repository Deposit Licence Agreement
rioxxterms.freetoread.startdate2100-01-01


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