Non-separable Spatio-temporal Graph Kernels via SPDEs

Alexander V. Nikitin, St John, Arno Solin, Samuel Kaski
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:10640-10660, 2022.

Abstract

Gaussian processes (GPs) provide a principled and direct approach for inference and learning on graphs. However, the lack of justified graph kernels for spatio-temporal modelling has held back their use in graph problems. We leverage an explicit link between stochastic partial differential equations (SPDEs) and GPs on graphs, introduce a framework for deriving graph kernels via SPDEs, and derive non-separable spatio-temporal graph kernels that capture interaction across space and time. We formulate the graph kernels for the stochastic heat equation and wave equation. We show that by providing novel tools for spatio-temporal GP modelling on graphs, we outperform pre-existing graph kernels in real-world applications that feature diffusion, oscillation, and other complicated interactions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-nikitin22a, title = { Non-separable Spatio-temporal Graph Kernels via SPDEs }, author = {Nikitin, Alexander V. and John, St and Solin, Arno and Kaski, Samuel}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {10640--10660}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/nikitin22a/nikitin22a.pdf}, url = {https://proceedings.mlr.press/v151/nikitin22a.html}, abstract = { Gaussian processes (GPs) provide a principled and direct approach for inference and learning on graphs. However, the lack of justified graph kernels for spatio-temporal modelling has held back their use in graph problems. We leverage an explicit link between stochastic partial differential equations (SPDEs) and GPs on graphs, introduce a framework for deriving graph kernels via SPDEs, and derive non-separable spatio-temporal graph kernels that capture interaction across space and time. We formulate the graph kernels for the stochastic heat equation and wave equation. We show that by providing novel tools for spatio-temporal GP modelling on graphs, we outperform pre-existing graph kernels in real-world applications that feature diffusion, oscillation, and other complicated interactions. } }
Endnote
%0 Conference Paper %T Non-separable Spatio-temporal Graph Kernels via SPDEs %A Alexander V. Nikitin %A St John %A Arno Solin %A Samuel Kaski %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-nikitin22a %I PMLR %P 10640--10660 %U https://proceedings.mlr.press/v151/nikitin22a.html %V 151 %X Gaussian processes (GPs) provide a principled and direct approach for inference and learning on graphs. However, the lack of justified graph kernels for spatio-temporal modelling has held back their use in graph problems. We leverage an explicit link between stochastic partial differential equations (SPDEs) and GPs on graphs, introduce a framework for deriving graph kernels via SPDEs, and derive non-separable spatio-temporal graph kernels that capture interaction across space and time. We formulate the graph kernels for the stochastic heat equation and wave equation. We show that by providing novel tools for spatio-temporal GP modelling on graphs, we outperform pre-existing graph kernels in real-world applications that feature diffusion, oscillation, and other complicated interactions.
APA
Nikitin, A.V., John, S., Solin, A. & Kaski, S.. (2022). Non-separable Spatio-temporal Graph Kernels via SPDEs . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:10640-10660 Available from https://proceedings.mlr.press/v151/nikitin22a.html.

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