Discrimination between Gaussian process models: active learning and static constructions

Elham Yousefi (), Luc Pronzato (), Markus Hainy (), Werner Müller and Henry P. Wynn ()
Additional contact information
Elham Yousefi: Johannes Kepler University
Luc Pronzato: Laboratoire I3S - UMR 7271
Markus Hainy: Johannes Kepler University
Henry P. Wynn: London School of Economics

Statistical Papers, 2023, vol. 64, issue 4, No 14, 1275-1304

Abstract: Abstract The paper covers the design and analysis of experiments to discriminate between two Gaussian process models with different covariance kernels, such as those widely used in computer experiments, kriging, sensor location and machine learning. Two frameworks are considered. First, we study sequential constructions, where successive design (observation) points are selected, either as additional points to an existing design or from the beginning of observation. The selection relies on the maximisation of the difference between the symmetric Kullback Leibler divergences for the two models, which depends on the observations, or on the mean squared error of both models, which does not. Then, we consider static criteria, such as the familiar log-likelihood ratios and the Fréchet distance between the covariance functions of the two models. Other distance-based criteria, simpler to compute than previous ones, are also introduced, for which, considering the framework of approximate design, a necessary condition for the optimality of a design measure is provided. The paper includes a study of the mathematical links between different criteria and numerical illustrations are provided.

Keywords: Model discrimination; Gaussian random field; Kriging; 62K05; 60G15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-023-01436-x

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