Vecchia approximations of Gaussian-process predictions
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Gaussian processes (GPs) are highly flexible function estimators used for nonparametric regression, machine learning, and geospatial analysis, but they are computationally infeasible for large datasets. Vecchia approximations of GPs have been used to enable fast evaluation of the likelihood for parameter inference. Here, we study Vecchia approximations of GP predictions at observed and unobserved locations, including obtaining joint predictive distributions at large sets of locations. We propose a general Vecchia framework for GP predictions, which contains some novel and some existing special cases. We study the accuracy and computational properties of these computational approaches theoretically and numerically. We show that our new approaches exhibit linear computational complexity in the total number of locations. We also apply our methods to a satellite dataset of chlorophyll fluorescence.
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