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Solving Schrödinger Bridges via Maximum Likelihood.

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dc.contributor.authorVargas, Francisco
dc.contributor.authorThodoroff, Pierre
dc.contributor.authorLamacraft, Austen
dc.contributor.authorLawrence, Neil
dc.contributor.orcidVargas, Francisco [0000-0002-2714-3357]
dc.contributor.orcidThodoroff, Pierre [0000-0001-7791-217X]
dc.contributor.orcidLamacraft, Austen [0000-0002-0707-0488]
dc.contributor.orcidLawrence, Neil [0000-0001-9258-1030]
dc.date.accessioned2021-10-30T01:12:50Z
dc.date.available2021-10-30T01:12:50Z
dc.date.issued2021-08-31
dc.date.updated2021-10-30T01:12:49Z
dc.description.abstractThe Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. Our main contribution is the proof of equivalence between solving the SBP and an autoregressive maximum likelihood estimation objective. This formulation circumvents many of the challenges of density estimation and enables direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.
dc.identifier.citationEntropy (Basel, Switzerland), volume 23, issue 9
dc.identifier.doi10.17863/CAM.77532
dc.identifier.issn1099-4300
dc.identifier.otherPMC8464739
dc.identifier.other34573759
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/330088
dc.languageeng
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceessn: 1099-4300
dc.sourcenlmid: 101243874
dc.subjectMachine Learning
dc.subjectStochastic Control
dc.subjectSchrödinger Bridges
dc.titleSolving Schrödinger Bridges via Maximum Likelihood.
dc.typeArticle
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/T517847/1)
pubs.funder-project-idhuawei technology co (NA)
rioxxterms.licenseref.urihttps://creativecommons.org/licenses/by/4.0/
rioxxterms.versionVoR
rioxxterms.versionofrecord10.3390/e23091134

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