Problem
Research questions and friction points this paper is trying to address.
Graph Kernels
Temporal-Spatial Changes
Gaussian Processes
Non-separable Spatio-temporal Graph Kernels via SPDEs
🤖 AI Summary
Existing graph-based Gaussian processes lack effective kernel functions capable of modeling spatiotemporal coupling dynamics on graphs. Method: This paper introduces the first derivation framework for non-separable spatiotemporal graph kernels grounded in stochastic partial differential equations (SPDEs). By establishing an explicit connection between SPDEs and graph Gaussian processes—leveraging spectral graph theory—we derive two classes of non-separable kernels corresponding to the heat and wave equations, respectively, thereby overcoming the modeling limitations of conventional separable kernels in capturing spatiotemporal interactions. Contribution/Results: The proposed kernels significantly outperform state-of-the-art graph kernels on complex spatiotemporal graph tasks—including diffusion and oscillation processes—demonstrating superior expressive power and predictive accuracy in empirical evaluations. This work establishes a novel paradigm for spatiotemporal covariance modeling over graph-structured data.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
SPDEs
Gaussian Processes on Graphs
Temporal and Spatial Variations
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