Robust and Conjugate Spatio-Temporal Gaussian Processes

William Laplante, Matias Altamirano, Andrew B. Duncan, Jeremias Knoblauch, Francois-Xavier Briol
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:32562-32592, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-laplante25a, title = {Robust and Conjugate Spatio-Temporal {G}aussian Processes}, author = {Laplante, William and Altamirano, Matias and Duncan, Andrew B. and Knoblauch, Jeremias and Briol, Francois-Xavier}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {32562--32592}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/laplante25a/laplante25a.pdf}, url = {https://proceedings.mlr.press/v267/laplante25a.html}, 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.} }
Endnote
%0 Conference Paper %T Robust and Conjugate Spatio-Temporal Gaussian Processes %A William Laplante %A Matias Altamirano %A Andrew B. Duncan %A Jeremias Knoblauch %A Francois-Xavier Briol %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-laplante25a %I PMLR %P 32562--32592 %U https://proceedings.mlr.press/v267/laplante25a.html %V 267 %X 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.
APA
Laplante, W., Altamirano, M., Duncan, A.B., Knoblauch, J. & Briol, F.. (2025). Robust and Conjugate Spatio-Temporal Gaussian Processes. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:32562-32592 Available from https://proceedings.mlr.press/v267/laplante25a.html.

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