L2-Boosting for sensitivity analysis with dependent inputs

Magali Champion (1) , Gaëlle Chastaing (2, 3) , Sébastien Gadat (1) , Clémentine Prieur (2, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows

This paper is dedicated to the study of an estimator of the generalized Hoeffding decomposition. We build such an estimator using an empirical Gram-Schmidt approach and derive a consistency rate in a large dimensional setting. We then apply a greedy algorithm with these previous estimators to a sensitivity analysis. We also establish the consistency of this L2-boosting under sparsity assumptions of the signal to be analyzed. The paper concludes with numerical experiments, that demonstrate the low computational cost of our method, as well as its efficiency on the standard benchmark of sensitivity analysis.

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

Magali Champion, Gaëlle Chastaing, Sébastien Gadat, Clémentine Prieur. L2-Boosting for sensitivity analysis with dependent inputs. Statistica Sinica, 2015, 25 (4), pp.1477-1502. ⟨10.5705/ss.2013.310⟩. ⟨hal-01068729⟩