Scalable inference in SDEs by direct matching of the Fokker–Planck–Kolmogorov equation

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorSolin, Arnoen_US
dc.contributor.authorTamir, Ellaen_US
dc.contributor.authorVerma, Prakharen_US
dc.contributor.departmentComputer Science Professorsen_US
dc.contributor.departmentDepartment of Computer Scienceen_US
dc.date.accessioned2022-02-09T06:50:22Z
dc.date.available2022-02-09T06:50:22Z
dc.date.issued2021en_US
dc.description.abstractSimulation-based techniques such as variants of stochastic Runge–Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and non-parametric models, and neural SDEs. Stochastic Runge–Kutta relies on the use of sampling schemes that can be inefficient in high dimensions. We address this issue by revisiting the classical SDE literature and derive direct approximations to the (typically intractable) Fokker–Planck–Kolmogorov equation by matching moments. We show how this workflow is fast, scales to high-dimensional latent spaces, and is applicable to scarce-data applications, where a non-parametric SDE with a driving Gaussian process velocity field specifies the model.en
dc.description.versionPeer revieweden
dc.format.extent13
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationSolin , A , Tamir , E & Verma , P 2021 , Scalable inference in SDEs by direct matching of the Fokker–Planck–Kolmogorov equation . in Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021) . Advances in Neural Information Processing Systems , Morgan Kaufmann Publishers , Conference on Neural Information Processing Systems , Virtual, Online , 06/12/2021 . < https://papers.nips.cc/paper/2021/hash/03e4d3f831100d4355663f3d425d716b-Abstract.html >en
dc.identifier.issn1049-5258
dc.identifier.otherPURE UUID: 377234a1-2bcc-4fcf-934d-a8a4a5248ed5en_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/377234a1-2bcc-4fcf-934d-a8a4a5248ed5en_US
dc.identifier.otherPURE LINK: https://papers.nips.cc/paper/2021/hash/03e4d3f831100d4355663f3d425d716b-Abstract.htmlen_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/79020224/SCI_Solin_etal_NeurIPS_2021_scalable_inference_in_sdes_by_direct_matching_of_the_fokkerplanckkolmogorov_equation_Paper.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/112920
dc.identifier.urnURN:NBN:fi:aalto-202202091813
dc.language.isoenen
dc.publisherMorgan Kaufmann Publishers
dc.relation.ispartofConference on Neural Information Processing Systemsen
dc.relation.ispartofseriesAdvances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)en
dc.relation.ispartofseriesAdvances in Neural Information Processing Systemsen
dc.rightsopenAccessen
dc.titleScalable inference in SDEs by direct matching of the Fokker–Planck–Kolmogorov equationen
dc.typeConference article in proceedingsfi
dc.type.versionpublishedVersion
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