Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Features

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorSolin, Arnoen_US
dc.contributor.authorKok, Manonen_US
dc.contributor.departmentDepartment of Computer Scienceen
dc.contributor.groupauthorProfessorship Solin A.en
dc.contributor.organizationDelft University of Technologyen_US
dc.date.accessioned2020-01-17T13:32:04Z
dc.date.available2020-01-17T13:32:04Z
dc.date.issued2019en_US
dc.description.abstractGaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We solve a Fourier-like generalised harmonic feature representation of the GP prior in the domain of interest, which both constrains the GP and attains a low-rank representation that is used for speeding up inference. The method scales as O(nm^2) in prediction and O(m^3) in hyperparameter learning for regression, where n is the number of data points and m the number of features. Furthermore, we make use of the variational approach to allow the method to deal with non-Gaussian likelihoods. The experiments cover both simulated and empirical data in which the boundary conditions allow for inclusion of additional physical information.en
dc.description.versionPeer revieweden
dc.format.extent2193-2202
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationSolin, A & Kok, M 2019, Know Your Boundaries : Constraining Gaussian Processes by Variational Harmonic Features . in Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) . Proceedings of Machine Learning Research, vol. 89, JMLR, pp. 2193-2202, International Conference on Artificial Intelligence and Statistics, Naha, Japan, 16/04/2019 . < http://proceedings.mlr.press/v89/solin19a.html >en
dc.identifier.issn2640-3498
dc.identifier.otherPURE UUID: cdfa86a8-d403-4f67-bf29-624a6019123aen_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/cdfa86a8-d403-4f67-bf29-624a6019123aen_US
dc.identifier.otherPURE LINK: http://proceedings.mlr.press/v89/solin19a.htmlen_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/40208954/Solin19a.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/42573
dc.identifier.urnURN:NBN:fi:aalto-202001171688
dc.language.isoenen
dc.publisherPMLR
dc.relation.ispartofInternational Conference on Artificial Intelligence and Statisticsen
dc.relation.ispartofseriesProceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS)en
dc.relation.ispartofseriesProceedings of Machine Learning Researchen
dc.relation.ispartofseriesVolume 89en
dc.rightsopenAccessen
dc.titleKnow Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Featuresen
dc.typeConference article in proceedingsfi
dc.type.versionpublishedVersion
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