Reproducing kernels for spaces of zero mean functions. Application to sensitivity analysis

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

1 CROCUS-ENSMSE - Equipe : Calcul de Risque, Optimisation et Calage par Utilisation de Simulateurs
2 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
4 LA MUSE - Laboratoire de Mathématiques Unifiées de Saint-Etienne

Given a Reproducing Kernel Hilbert Space (H, h., .i) of real-valued functions and a suitable measure μ over the source space, we decompose H as sum of a subspace of centered functions for μ and its orthogonal in H. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the minimal norm interpolator can be elegantly derived. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.

Domaines: Autres [stat.ML]

Nicolas Durrande, David Ginsbourger, Olivier Roustant, Laurent Carraro. Reproducing kernels for spaces of zero mean functions. Application to sensitivity analysis. 2011. ⟨hal-00601472v1⟩