Randomized pick-freeze for sparse Sobol indices estimation in high   dimension
  This article investigates a new procedure to estimate the influence of each variable of a given function defined on a high-dimensional space. More precisely, we are concerned with describing a function of a large number $p$ of parameters that depends only on a small number $s$ of them. Our proposed method is an unconstrained $\ell_{1}$-minimization based on the Sobol's method. We prove that, with only $\mathcal O(s\log p)$ evaluations of $f$, one can find which are the relevant parameters. 
Yohann De Castro (LM-Orsay), Alexandre Janon (LM-Orsay, - M\'ethodes   d'Analyse Stochastique des Codes et Traitements Num\'...
stat.CO math.ST stat.AP stat.ME stat.TH