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.
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 language | English |
|---|---|
| Title of host publication | Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS 2019) |
| Editors | Kamalika Chaudhuri, Masashi Sugiyama |
| Publisher | MLR Press |
| Number of pages | 10 |
| Publication status | Published - 2019 |
| Event | AISTATS 2019 2019: 22nd International Conference on Artificial Intelligence and Statistics - Naha, Okinawa, Japan Duration: 16 Apr 2019 → 18 Apr 2019 |
Publication series
| Name | Proceedings of Machine Learning Research (PMLR) |
|---|---|
| Volume | 89 |
| ISSN (Electronic) | 2640-3498 |
Conference
| Conference | AISTATS 2019 2019: 22nd International Conference on Artificial Intelligence and Statistics |
|---|---|
| Country/Territory | Japan |
| City | Naha, Okinawa |
| Period | 16/04/19 → 18/04/19 |