Non-separable Spatio-temporal Graph Kernels via SPDEs
This provides novel tools for spatio-temporal Gaussian process modeling on graphs, addressing a bottleneck in graph-based inference and learning.
The paper tackled the lack of justified graph kernels for spatio-temporal modeling by introducing non-separable spatio-temporal graph kernels derived from stochastic partial differential equations (SPDEs), and showed that these kernels outperform pre-existing ones in real-world applications involving diffusion and oscillation.
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.