Robust and Conjugate Spatio-Temporal Gaussian Processes
William Laplante, Matias Altamirano, Andrew B. Duncan, Jeremias Knoblauch, Francois-Xavier Briol
Abstract
State-space formulations allow for Gaussian process (GP) regression with linear-in-time computational cost in spatio-temporal settings, but performance typically suffers in the presence of outliers. In this paper, we adapt and specialise the *robust and conjugate GP (RCGP)* framework of Altamirano et al. (2024) to the spatio-temporal setting. In doing so, we obtain an outlier-robust spatio-temporal GP with a computational cost comparable to classical spatio-temporal GPs. We also overcome the three main drawbacks of RCGPs: their unreliable performance when the prior mean is chosen poorly, their lack of reliable uncertainty quantification, and the need to carefully select a hyperparameter by hand. We study our method extensively in finance and weather forecasting applications, demonstrating that it provides a reliable approach to spatio-temporal modelling in the presence of outliers.
BibTeX
@inproceedings{
laplante2025robust,
title={Robust and Conjugate Spatio-Temporal Gaussian Processes},
author={William Laplante and Matias Altamirano and Andrew B. Duncan and Jeremias Knoblauch and Francois-Xavier Briol},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=YG84SWm7gn}
}