Total interaction indices for the decomposition of functions with high complexity

Jana Fruth (1) , Olivier Roustant (2, 3) , Sonja Kuhnt (1)

1 TU - Technische Universität Dortmund [Dortmund]
2 CROCUS-ENSMSE - Equipe : Calcul de Risque, Optimisation et Calage par Utilisation de Simulateurs
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

We consider functions of high complexity that cannot be reduced to main effects and second order interactions. In this context, identifying groups of variables that have no interaction together can be done with the total interaction index, which quantifies the total contribution brought by a couple of variables. The aim of the paper is to investigate these indices. At the theoretical level, we show connections with total indices and closed indices, and prove that the total interaction index can be computed by integrating the second interaction of a 2-dimensional function obtained by cutting the original one. Then, we focus on computational issues and compare three different methods on several analytical test functions. The superiority of the so-called fixing method is demonstrated to estimate total interaction indices of low value.

Mots clés: FANOVA decomposition; Sobol indices; Complexity; Computer experiments

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Calcul [stat.CO]

Jana Fruth, Olivier Roustant, Sonja Kuhnt. Total interaction indices for the decomposition of functions with high complexity. 2011. ⟨hal-00631066v1⟩