This article investigates selection of variables in high-dimension from a non-parametric regression model. In many concrete situations, we are concerned with estimating a non-parametric regression function that may depend on a large number of inputs variables. Unlike standard procedures, we do not assume that belongs to a class of regular functions (Hölder, Sobolev, ...), yet we assume that is a square-integrable function with respect to a known product measure. Furthermore, observe that, in some situations, only a small number of the coordinates actually affects in an additive manner. In this context, we prove that, with only random evaluations of , one can find which are the relevant input variables with overwhelming probability. Our proposed method is an unconstrained -minimization procedure based on the Sobol’s method. One step of this procedure relies on support recovery using -minimization and thresholding. More precisely, we use a thresholded-LASSO to faithfully uncover the significant input variables. In this frame, we prove that one can relax the mutual incoherence property (known to require observations) and still ensure faithful recovery from observations for any .
DOI : 10.1051/ps/2015013
Mots clés : Sensitivity analysis, Sobol indices, high-dimensional statistics, LASSO, Monte-Carlo method
@article{PS_2015__19__725_0, author = {de Castro, Yohann and Janon, Alexandre}, title = {Randomized pick-freeze for sparse {Sobol} indices estimation in high dimension}, journal = {ESAIM: Probability and Statistics}, pages = {725--745}, publisher = {EDP-Sciences}, volume = {19}, year = {2015}, doi = {10.1051/ps/2015013}, zbl = {1392.62111}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2015013/} }
TY - JOUR AU - de Castro, Yohann AU - Janon, Alexandre TI - Randomized pick-freeze for sparse Sobol indices estimation in high dimension JO - ESAIM: Probability and Statistics PY - 2015 SP - 725 EP - 745 VL - 19 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2015013/ DO - 10.1051/ps/2015013 LA - en ID - PS_2015__19__725_0 ER -
%0 Journal Article %A de Castro, Yohann %A Janon, Alexandre %T Randomized pick-freeze for sparse Sobol indices estimation in high dimension %J ESAIM: Probability and Statistics %D 2015 %P 725-745 %V 19 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2015013/ %R 10.1051/ps/2015013 %G en %F PS_2015__19__725_0
de Castro, Yohann; Janon, Alexandre. Randomized pick-freeze for sparse Sobol indices estimation in high dimension. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 725-745. doi : 10.1051/ps/2015013. http://www.numdam.org/articles/10.1051/ps/2015013/
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