Robust and Conjugate Spatio-Temporal Gaussian Processes

TL;DR

This paper develops a robust, outlier-resistant spatio-temporal Gaussian process model that maintains computational efficiency and improves reliability in uncertainty quantification, especially in finance and weather forecasting.

Contribution

It adapts the robust conjugate GP framework to spatio-temporal data, addressing key drawbacks and enhancing performance in outlier-prone scenarios.

Findings

Effective outlier robustness in finance and weather data

Maintains computational cost comparable to classical models

Improves uncertainty quantification reliability

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.