Spectral approximation of the IMSE criterion for optimal designs in kernel-based interpolation models

Gauthier, Bertrand ORCID: https://orcid.org/0000-0001-5469-814X and Pronzato, Luc 2014. Spectral approximation of the IMSE criterion for optimal designs in kernel-based interpolation models. SIAM/ASA Journal on Uncertainty Quantification 2 (1) , pp. 805-825. 10.1137/130928534

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Abstract

We address the problem of computing integrated mean-squared error (IMSE)-optimal designs for random field interpolation models. A spectral representation of the IMSE criterion is obtained from the eigendecomposition of the integral operator defined by the covariance kernel of the random field and integration measure considered. The IMSE can then be approximated by spectral truncation, and bounds on the error induced by this truncation are given. We show how the IMSE and truncated-IMSE can easily be computed when a quadrature rule is used to approximate the integrated MSE and the design space is restricted to a subset of quadrature points. Numerical experiments are carried out and indicate (i) that retaining a small number of eigenpairs (in regard to the quadrature size) is often sufficient to obtain good approximations of IMSE-optimal quadrature-designs when optimizing the truncated criterion and (ii) that optimal quadrature-designs generally give efficient approximations of the true optimal designs for the quadrature approximation of the IMSE.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	2166-2525
Date of Acceptance:	30 October 2014
Last Modified:	02 Nov 2022 10:13
URI:	https://orca.cardiff.ac.uk/id/eprint/97834

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