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Reports (Research Report) Year : 2014

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

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Yohann de Castro
Alexandre Janon
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#### 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.

### Dates and versions

hal-00962473 , version 1 (21-03-2014)

### Identifiers

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

### Cite

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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