A specific kriging kernel for dimensionality reduction: Isotropic by group kernel

Christophette Blanchet-Scalliet (1) , Céline Helbert (1, 2) , Mélina Ribaud (1) , Céline Vial (1)

1 ICJ - Institut Camille Jordan
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

In the context of computer experiments, metamodels are largely used to represent the output of computer codes. Among these models, Gaussian process regression (kriging) is very efficient see e.g Snelson (2008). In high dimension that is with a large number of input variables , but with few observations the classical anisotropic kriging becomes inefficient and sometimes completely wrong. One way to overcome this drawback is to use the isotropic kernel which is more robust because it estimates not as many parameters. However this model is too restrictive. The aim of this paper is to construct a model between these two, that is at the same time a robust and a flexible model. These two skills are necessary for a model in high dimension. We propose a kernel which is an answer to these requests and that we call isotropic by group kernel. This kernel is a tensor product of few isotropic kernels built on well-chosen subgroup of variables. The number and the composition of the groups are found by an algorithm which explores different structures. The choice of the best model is based on the quality of prediction.

Mots clés: kriging; metamodel; kernel; isotropic; anisotropic; clustering; high dimen- sion

Domaines: Méthodologie [stat.ME]

Christophette Blanchet-Scalliet, Céline Helbert, Mélina Ribaud, Céline Vial. A specific kriging kernel for dimensionality reduction: Isotropic by group kernel. 2017. ⟨hal-01496521v2⟩