Know Your Boundaries

Constraining Gaussian Processes by Variational Harmonic Features

Conference paper (2019)

Authors

Arno Solin Aalto University
M. Kok Team Jan-Willem van Wingerden - Mechanical, Maritime and Materials Engineering
Manon Kok Team Jan-Willem van Wingerden - Mechanical, Maritime and Materials Engineering
Research Group
Team Jan-Willem van Wingerden (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2019 Arno Solin, M. Kok
More Info
expand_more

Published Date

2019

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Jan-Willem van Wingerden

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 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.

Files

Article.pdf
(pdf | 1.72 Mb)
Unknown license