Non-separable spatio-temporal graph kernels via SPDEs

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Journal Title
Journal ISSN
Volume Title
Conference article in proceedings
Date
2022
Major/Subject
Mcode
Degree programme
Language
en
Pages
10640-10660
Series
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research, Volume 151
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.
Description
Keywords
Gaussian process (GP), Graphs, machine learning, spatio-temporal analysis
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Citation
Nikitin, A, John, ST, Solin, A & Kaski, S 2022, Non-separable spatio-temporal graph kernels via SPDEs . in Proceedings of The 25th International Conference on Artificial Intelligence and Statistics . Proceedings of Machine Learning Research, vol. 151, JMLR, pp. 10640-10660, International Conference on Artificial Intelligence and Statistics, Valencia, Spain, 28/03/2022 . < https://proceedings.mlr.press/v151/nikitin22a.html >