# Randomized pick-freeze for sparse Sobol indices estimation in high dimension

1 Probabilités et Statistique
LM-Orsay - Laboratoire de Mathématiques d'Orsay
Abstract : 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.
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Cited literature [28 references]

https://hal.inria.fr/hal-00962473
Contributor : Alexandre Janon <>
Submitted on : Friday, March 21, 2014 - 1:03:06 PM
Last modification on : Thursday, January 11, 2018 - 6:26:42 AM
Document(s) archivé(s) le : Saturday, June 21, 2014 - 11:15:38 AM

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• HAL Id : hal-00962473, version 1
• ARXIV : 1403.5537

### Citation

Yohann de Castro, Alexandre Janon. Randomized pick-freeze for sparse Sobol indices estimation in high dimension. [Research Report] 2014. ⟨hal-00962473⟩

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