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David Ginsbourger; Xavier Bay; Olivier Roustant; Laurent Carraro
Argumentwise invariant kernels for the approximation of invariant functions
Annales de la faculté des sciences de Toulouse Sér. 6, 21 no. 3 (2012), p. 501-527, doi: 10.5802/afst.1343
Article PDF | Analyses MR 3076410 | Zbl pre06125983

Résumé - Abstract

Nous considérons le problème d’approximation par méthodes à noyaux de fonctions invariantes sous l’action d’un groupe fini. Nous introduisons les noyaux doublement invariants, et montrons qu’ils caractérisent les champs aléatoires centrés de carré intégrable à trajectoires invariantes, ainsi que les espaces de Hilbert à noyau reproduisant de fonctions invariantes. Deux classes particulières de noyaux doublement invariants sont considérées, basées respectivement sur un domaine fondamental ou sur une double somme sur les orbites. Nous établissons ensuite des propriétés d’invariance pour les modèles de Krigeage et les simulations consitionnelles associés. L’applicabilité et les avantages de tels noyaux sont illustrés sur plusieurs exemples, incluant une fonction symétrique issue d’un problème de fiabilité des structures.

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