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Low-rank approximation is a popular strategy to tackle the "big n problem"associated with large-scale Gaussian process regressions. Basis functions fordeveloping low-rank structures are crucial and should be carefully specified.Predictive processes simplify the problem by inducing basis functions with acovariance function and a set of knots. The existing literature suggestscertain practical implementations of knot selection and covariance estimation;however, theoretical foundations explaining the influence of these two factorson predictive processes are lacking. In this paper, the asymptotic predictionperformance of the predictive process and Gaussian process predictions isderived and the impacts of the selected knots and estimated covariance arestudied. We suggest the use of support points as knots, which best representdata locations. Extensive simulation studies demonstrate the superiority ofsupport points and verify our theoretical results. Real data of precipitationand ozone are used as examples, and the efficiency of our method over otherwidely used low-rank approximation methods is verified.

Large-Scale Low-Rank Gaussian Process Prediction with Support Points