Discrimination between Gaussian process models: active learning and static constructions

Elham Yousefi, Luc Pronzato, Markus Hainy, Werner Müller and Henry P. Wynn

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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: Gaussian random field; Kriging; model discrimination (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2023-08-01
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Published in Statistical Papers, 1, August, 2023, 64(4), pp. 1275 - 1304. ISSN: 0932-5026

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Related works:
Journal Article: Discrimination between Gaussian process models: active learning and static constructions (2023)
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