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.
Original languageEnglish
Title of host publicationProceedings of The 25th International Conference on Artificial Intelligence and Statistics
Publication statusPublished - 2022
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Artificial Intelligence and Statistics - Valencia, Spain
Duration: 28 Mar 202230 Mar 2022
Conference number: 25

Publication series

NameProceedings of Machine Learning Research
ISSN (Electronic)2640-3498


ConferenceInternational Conference on Artificial Intelligence and Statistics
Abbreviated titleAISTATS


  • Gaussian process (GP)
  • Graphs
  • machine learning
  • spatio-temporal analysis


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