  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
settings.
  Then, we apply a greedy algorithm with these previous estimators to
Sensitivity Analysis. We also establish the consistency of this $\mathbb
L_2$-boosting up to sparsity assumptions on the signal to analyse. We end the
paper with numerical experiments, which demonstrates the low computational cost
of our method as well as its efficiency on standard benchmark of Sensitivity
Analysis.
