Solving Schrödinger Bridges via Maximum Likelihood.

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dc.creatorVargas, Francisco
dc.creatorThodoroff, Pierre
dc.creatorLamacraft, Austen
dc.creatorLawrence, Neil
dc.date2021-11-13T00:30:45Z
dc.date2021-11-13T00:30:45Z
dc.date2021-08-31
dc.date.accessioned2026-08-03T03:48:40Z
dc.descriptionThe 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.formatElectronic
dc.formatapplication/pdf
dc.identifier1099-4300
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/330633
dc.identifier10.17863/CAM.78077
dc.identifier1099-4300
dc.identifier.urihttps://repo.dare.co.zw/handle/123456789/181043
dc.languageeng
dc.languageeng
dc.publisherMDPI
dc.publisherhttps://doi.org/10.3390/e23091134
dc.rightsAttribution 4.0 International
dc.rightshttps://creativecommons.org/licenses/by/4.0/
dc.subjectSchrödinger bridges
dc.subjectmachine learning
dc.subjectstochastic control
dc.titleSolving Schrödinger Bridges via Maximum Likelihood.
dc.typeArticle

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