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Data-Driven Model Reduction, Scientific Frontiers, and Applications ()

Rui Tuo, Wm Michael Barnes Department of Industrial & Systems Engineering
Scalable algorithms for Gaussian Process Regression via Kernel Packets


In this talk, I will introduce an exact and scalable algorithm for one-dimensional Gaussian process regression under Matérn correlations with half-integer smoothness. The proposed algorithm requires only O(n) operations and O(n) storage. The algorithm is based on a new theoretical result on these kernel functions, which shows that suitable rearrangement of these functions can produce a compactly supported function, called a “kernel packet.” Using a set of kernel packets as basis functions leads to a sparse representation of the covariance matrix that results in the proposed algorithm. Via model reduction and tensor product techniques, we also propose efficient and accurate algorithms for Gaussian process regression in general dimensions.