Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Features

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Conference article in proceedings
Date
2019
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Mcode
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Language
en
Pages
2193-2202
Series
Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), Proceedings of Machine Learning Research, Volume 89
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.
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Solin, 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 >