Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Features

Arno Solin, Manon Kok

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

1 Citation (Scopus)
14 Downloads (Pure)

Abstract

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.
Original languageEnglish
Title of host publicationProceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS)
PublisherJMLR W&CP
Pages2193-2202
Publication statusPublished - 2019
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Artificial Intelligence and Statistics - Naha, Japan
Duration: 16 Apr 201918 Apr 2019
Conference number: 22

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR
Volume89
ISSN (Print)2640-3498

Conference

ConferenceInternational Conference on Artificial Intelligence and Statistics
Abbreviated titleAISTATS
CountryJapan
CityNaha
Period16/04/201918/04/2019

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