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Spatio-Temporal Inference of Dynamical Gaussian Processes Over Graphs

Inference of spatio-temporal processes over graphs arises in a gamut of network science-related applications, including smart transportation, climate forecasting, and neuroscience. Given observations over a subset of the nodes due to sampling cost or privacy considerations, extrapolation of time-varying signals over the unobserved nodes can be realized by leveraging their spatio-temporal correlations across the graph. The present contribution introduces a novel multi-output Gaussian process (GP) autoregressive model to not only capture the temporal dynamics of the nodal process from slot to slot, but also account for the per-slot spatial correlation across nodes using the family of Laplacian kernels. To alleviate the computational burden of batch GP-based learning, a scalable solver is devised to estimate the missing values with the online arrival of nodal observations. Tests with real data showcase the merits of the proposed method relative to the existing alternatives.