Integration-free Kernels for Equivariant Gaussian Process Modelling

Tim Steinert, David Ginsbourger, August Lykke-Møller, Ove Christiansen, Henry Moss
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:56874-56898, 2025.

Abstract

We study the incorporation of equivariances into vector-valued GPs and more general classes of random field models. While kernels guaranteeing equivariances have been investigated previously, their evaluation is often computationally prohibitive due to required integrations over the involved groups. In this work, we provide a kernel characterization of stochastic equivariance for centred second-order vector-valued random fields and we construct integration-free equivariant kernels based on the notion of fundamental regions of group actions. We establish data-efficient and computationally lightweight GP models for velocity fields and molecular electric dipole moments and demonstrate that proposed integration-free kernels may also be leveraged to extract equivariant components from data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-steinert25a, title = {Integration-free Kernels for Equivariant {G}aussian Process Modelling}, author = {Steinert, Tim and Ginsbourger, David and Lykke-M{\o}ller, August and Christiansen, Ove and Moss, Henry}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {56874--56898}, 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/steinert25a/steinert25a.pdf}, url = {https://proceedings.mlr.press/v267/steinert25a.html}, abstract = {We study the incorporation of equivariances into vector-valued GPs and more general classes of random field models. While kernels guaranteeing equivariances have been investigated previously, their evaluation is often computationally prohibitive due to required integrations over the involved groups. In this work, we provide a kernel characterization of stochastic equivariance for centred second-order vector-valued random fields and we construct integration-free equivariant kernels based on the notion of fundamental regions of group actions. We establish data-efficient and computationally lightweight GP models for velocity fields and molecular electric dipole moments and demonstrate that proposed integration-free kernels may also be leveraged to extract equivariant components from data.} }
Endnote
%0 Conference Paper %T Integration-free Kernels for Equivariant Gaussian Process Modelling %A Tim Steinert %A David Ginsbourger %A August Lykke-Møller %A Ove Christiansen %A Henry Moss %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-steinert25a %I PMLR %P 56874--56898 %U https://proceedings.mlr.press/v267/steinert25a.html %V 267 %X We study the incorporation of equivariances into vector-valued GPs and more general classes of random field models. While kernels guaranteeing equivariances have been investigated previously, their evaluation is often computationally prohibitive due to required integrations over the involved groups. In this work, we provide a kernel characterization of stochastic equivariance for centred second-order vector-valued random fields and we construct integration-free equivariant kernels based on the notion of fundamental regions of group actions. We establish data-efficient and computationally lightweight GP models for velocity fields and molecular electric dipole moments and demonstrate that proposed integration-free kernels may also be leveraged to extract equivariant components from data.
APA
Steinert, T., Ginsbourger, D., Lykke-Møller, A., Christiansen, O. & Moss, H.. (2025). Integration-free Kernels for Equivariant Gaussian Process Modelling. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:56874-56898 Available from https://proceedings.mlr.press/v267/steinert25a.html.

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