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Kriging and Invariances


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Titre du congrès :ENBIS8 - European Network for Business and Industrial Statistics
Ville du congrès :Athènes
Date du congrès :21/09/2008

Type de document > *Congrès/colloque

Mots clés > covariance noyau, invariant, krigeage

Unité de recherche > IRSN/DSU/SEC/LERD

Auteurs > GINSBOURGER David, RICHET Yann, ROUSTANT Olivier

Date de publication > 25/09/2008

Résumé

Learning a deterministic function using a gaussian process (Kriging) relies on the selection of a covariance kernel. When some prior information is available concerning symmetries of the function to be approximated, it is clearly unreasonable not to use it in the choice of the kernel or covariance function. We propose a characterization of the kernels which associated gaussian processes have their paths invariant under the action of a finite group of transformations. We then give an example of such symmetrical processes, built on the basis of stationary gaussian processes, and having interesting regularity properties. The applicability of the latter methodology is finally demonstrated with the help of toy examples and of an industrial test-case.