Gaussian Process Dynamical Modeling for Adaptive Inference Over Graphs

Graph-based inference 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 costs or privacy considerations, extrapolation of time-varying signals over the unobserved nodes can be realized by leveraging their spatio-temporal correlations across the graph. Building on a recently proposed Gaussian process (GP) auto-regressive model to capture spatio-temporal dynamics across slots, the present work further pursues an adaptive framework by ensembling a candidate set of such dynamical models, each representing a unique dynamic pattern of the sought process. With nodal observation arriving on-the-fly, the proposed method simultaneously estimates the missing nodal values and selects the fitted dynamical model via data-adaptive weights. Tests with real data showcase the merits of the proposed method.