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Statistica Sinica 25 (2015), 1477-1502

L2-BOOSTING FOR SENSITIVITY ANALYSIS
WITH DEPENDENT INPUTS
Magali Champion1,3, Gaelle Chastaing1,2, Sébastien Gadat4
and Clémentine Prieur2
1Université Paul Sabatier, 2Université Grenoble Alpes CNRS,
3INRA and 4Université Toulouse I Capitole

Abstract: This paper is dedicated to the study of an estimator of the generalized Hoeffding decomposition. We build 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.

Key words and phrases: L2-boosting, convergence, dependent variables, generalized ANOVA decomposition, sensitivity analysis.

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