# Sparse classification boundaries

Abstract : Given a training sample of size $m$ from a $d$-dimensional population, we wish to allocate a new observation $Z\in \R^d$ to this population or to the noise. We suppose that the difference between the distribution of the population and that of the noise is only in a shift, which is a sparse vector. For the Gaussian noise, fixed sample size $m$, and the dimension $d$ that tends to infinity, we obtain the sharp classification boundary and we propose classifiers attaining this boundary. We also give extensions of this result to the case where the sample size $m$ depends on $d$ and satisfies the condition $(\log m)/\log d \to \gamma$, $0\le \gamma<1$, and to the case of non-Gaussian noise satisfying the Cramér condition.
Keywords :
Type de document :
Pré-publication, Document de travail
2009
Domaine :

https://hal.archives-ouvertes.fr/hal-00371237
Contributeur : Christophe Pouet <>
Soumis le : vendredi 27 mars 2009 - 09:24:47
Dernière modification le : vendredi 10 février 2017 - 01:12:40
Document(s) archivé(s) le : jeudi 10 juin 2010 - 18:54:42

### Fichiers

IngsterPouetTsybakov2009.pdf
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### Identifiants

• HAL Id : hal-00371237, version 1
• ARXIV : 0903.4807

### Citation

Yuri Ingster, Christophe Pouet, Alexandre Tsybakov. Sparse classification boundaries. 2009. <hal-00371237>

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