Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Features

Arno Solin, Manon Kok

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference contributionScientificvertaisarvioitu

1 Sitaatiot (Scopus)
14 Lataukset (Pure)

Abstrakti

Gaussian 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.
AlkuperäiskieliEnglanti
OtsikkoProceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS)
KustantajaJMLR W&CP
Sivut2193-2202
TilaJulkaistu - 2019
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisuussa
TapahtumaInternational Conference on Artificial Intelligence and Statistics - Naha, Japani
Kesto: 16 huhtikuuta 201918 huhtikuuta 2019
Konferenssinumero: 22

Julkaisusarja

NimiProceedings of Machine Learning Research
KustantajaPMLR
Vuosikerta89
ISSN (painettu)2640-3498

Conference

ConferenceInternational Conference on Artificial Intelligence and Statistics
LyhennettäAISTATS
MaaJapani
KaupunkiNaha
Ajanjakso16/04/201918/04/2019

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