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.

Lay Summary: Spatio-temporal models are used to study changes in phenomena like weather or market activity over time, but they often fail when the data include unusual observations. We develop a more robust approach that stays accurate and efficient, even with messy data. This improves prediction in fields such as meteorology and finance, where outliers are prevalent.

Link To Code: https://github.com/williamlaplante/ST-RCGP

Primary Area: Probabilistic Methods->Gaussian Processes

Keywords: Gaussian Processes, Robustness, Spatio-Temporal Analysis, Generalised Bayes

Submission Number: 3877