Kernels and designs for modelling invariant functions: From group invariance to additivity

David Ginsbourger (1) , Nicolas Durrande (2) , Olivier Roustant (3, 4, 5)

1 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]
2 SITraN - Sheffield Institute for Translational Neuroscience
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
4 DEMO-ENSMSE - Département Décision en Entreprise : Modélisation, Optimisation
5 CROCUS-ENSMSE - Equipe : Calcul de Risque, Optimisation et Calage par Utilisation de Simulateurs

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of "axis designs" outperfoms latin hypercubes in terms of the IMSE criterion.

Mots clés: Kriging; composition operators; decompositions; interactions

Domaines: Modélisation et simulation; Analyse fonctionnelle [math.FA]; Probabilités [math.PR]; Machine Learning [stat.ML]; Méthodologie [stat.ME]

David Ginsbourger, Nicolas Durrande, Olivier Roustant. Kernels and designs for modelling invariant functions: From group invariance to additivity. MODA-10, Physica-Verlag HD, 2013. ⟨hal-00731657⟩