On false discovery rate thresholding for classification under sparsity

2011/06/30 by Pierre Neuvial, Etienne Roquain
Mathematics · #Bayes' theorem #False discovery rate #Function (biology) #Gaussian #Laplace transform #Oracle #Property (philosophy) #Rate of convergence #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Thresholding #stat.ME

paper · pdf · doi:10.1214/12-aos1042

published as Annals of Statistics (2012) Vol. 40, No. 5, 2572-2600

openalex publication_date 2012/10/01 · arxiv created 2013/03/05 · arxiv updated 2013/03/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

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 α_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.

Citations

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