Robust and Conjugate Spatio-Temporal Gaussian Processes

• URL: http://arxiv.org/abs/2502.02450v1
• Date: Tue, 04 Feb 2025 16:16:01 GMT
• Title: Robust and Conjugate Spatio-Temporal Gaussian Processes
• Authors: William Laplante, Matias Altamirano, Andrew Duncan, Jeremias Knoblauch, François-Xavier Briol,
• Abstract summary: We adapt and specialise the robust RCGP framework of Altamirano al et al. We obtain an-robust-temporal GP with a comparable computational cost to classical-temporal GPs. We study our method extensively in finance and weather applications.
• Score: 7.0029761533393495
• License:
• 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.

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