Efficient training of Gaussian processes with tensor product structure

Josie Koenig (), Max Pfeffer () and Martin Stoll ()
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Josie Koenig: University of Potsdam
Max Pfeffer: University of Göttingen
Martin Stoll: TU Chemnitz

Computational Optimization and Applications, 2025, vol. 92, issue 2, No 6, 563-587

Abstract: Abstract To determine the optimal set of hyperparameters of a Gaussian process based on a large number of training data, both a linear system and a trace estimation problem must be solved. In this paper, we focus on establishing numerical methods for the case where the covariance matrix is given as the sum of possibly multiple Kronecker products, i.e., can be identified as a tensor. As such, we will represent this operator and the training data in the tensor train format. Based on the AMEn method and Krylov subspace methods, we derive an efficient scheme for computing the matrix functions required for evaluating the gradient and the objective function in hyperparameter optimization.

Keywords: Gaussian process; Tensor train; Trace estimation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-025-00707-7

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