Total interaction index: A variance-based sensitivity index for interaction screening

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

1 TU - Technische Universität Dortmund [Dortmund]
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 DEMO-ENSMSE - Département Décision en Entreprise : Modélisation, Optimisation

We consider the problem of investigating the interaction structure of a multivariate function, possibly containing high order interactions, through variance-based indices. By analogy with the total index, used to detect the most influential variables, a screening of interactions can be done with the so-called total interaction index (TII), defined as the superset importance of a pair of variables. Our aim is to investigate the TII. At the theoretical level, it is connected to total and closed indices, and it is shown that the TII is obtained by averaging the second order interaction of a 2-dimensional function obtained by fixing the original one. We then present several estimation methods and prove the asymptotical efficiency of an estimator from Liu and Owen (2006). Its superiority is also confirmed empirically. Finally, an application is given to recover a block-additive structure of a function, without knowledge about the interaction orders nor about the blocks.

Mots clés: Sensitivity analysis; FANOVA decomposition; Sobol indices; High-order interactions; Superset importance; Additive structure; Computer experiments

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

Jana Fruth, Olivier Roustant, Sonja Kuhnt. Total interaction index: A variance-based sensitivity index for interaction screening. 2012. ⟨hal-00631066v4⟩