L2-boosting on a generalized Hoeffding decomposition for dependent variables. Application to Sensitivity Analysis

Résumé

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 numerica l experiments, that demonstrate the low computational cost of our method, as well as its efficiency on the standard benchmark of sensitivity analysis.