Know Your Boundaries

Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Features

Solin, Arno (Aalto University)
Kok, M. (TU Delft Team Jan-Willem van Wingerden)

Chaudhuri, Kamalika (editor)
Sugiyama, Masashi (editor)

2019

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 lowrank representation that is used for speeding up inference. The method scales as O(nm2) in prediction and O(m3) 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.

http://resolver.tudelft.nl/uuid:86de4906-4d76-412c-8ce3-e1e8ad7ed56f

MLR Press

Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS 2019)

AISTATS 2019 2019: 22nd International Conference on Artificial Intelligence and Statistics, 2019-04-16 → 2019-04-18, Naha, Okinawa, Japan

Proceedings of Machine Learning Research (PMLR), 2640-3498, 89

Institutional Repository

conference paper

© 2019 Arno Solin, M. Kok