Work

On false discovery rate thresholding for classification under sparsity

Year: 2012

Type: article

Abstract: We study the properties of false discovery rate (FDR) thresholding, viewed as a classification procedure. The “$0$”-class (null) is assumed to have a known density while the “$1$”-class (alternative) is obtained from the “$0$”-class either by translation or by scaling. Furthermore, the “$1$”-class is assumed to have a small number of elements w.r.t. the “$0$”-class (sparsity). We focus on densities of the Subbotin family, including Gaussian and Laplace models. Nonasymptotic oracle inequalities are derived for the excess risk of FDR thresholding. These inequalities lead to explicit rates of convergence of the excess risk to zero, as the number $m$ of items to be classified tends to infinity and in a regime where the power of the Bayes rule is away from $0$ and $1$. Moreover, these theoretical investigations suggest an explicit choice for the target level $\alpha_{m}$ of FDR thresholding, as a function of $m$. Our oracle inequalities show theoretically that the resulting FDR thresholding adapts to the unknown sparsity regime contained in the data. This property is illustrated with numerical experiments.

Source: The Annals of Statistics

Authors: Pierre Neuvial, Etienne Roquain

Institutions: Université Pierre-et-Marie-Curie, Université d'Évry Val-d'Essonne

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Agence Nationale de la Recherche

Awards: Point processes, learning, nonparametric statistics and applications, DETECT: Nouvelles approches statistiques pour la vision artificielle et la bioinformatique

OpenAlex ID: W2025932509