A New Non-Separable Kernel for Spatio-Temporal Gaussian Process Regression

We adopt spatio-temporal Gaussian process regression (GPR) for prediction of PM2.5 concentrations at various spatial locations across India, and we compare its performance to purely temporal GPR. We design a new, non-separable spatiotemporal (ST) covariance kernel which can express dependence (i.e. coupling) between the spatial and temporal covariance structures. Specifically, we replace the separable weighted Euclidean norm—commonly used to achieve automatic relevance determination (ARD)—with a non-separable Mahalanobis norm in the squared exponential kernel function of the GP. We find that the spatio-temporal GPR (STGPR) task achieves better predictive performance at hold-out locations than purely temporal GPR at those locations. We also find that the new, non-separable ST exponential kernel significantly outperforms the separable ST kernel in this application.