Learning from MOM's principles: Le Cam's approach

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Lecue, Guillaume¹  Lerasle, Matthieu² 

[1] Univ Paris Saclay, CNRS, CREST, St Aubin, France

[2] Univ Paris Saclay, CNRS, Univ Paris Sud, Lab Math Orsay, St Aubin, France

关键词: Robust statistics;    Statistical learning;    High dimensional statistics;   

DOI  :  10.1016/j.spa.2018.11.024

来源: Elsevier

【 摘 要 】

New robust estimators are introduced, derived from median-of-means principle and Le Cam's aggregation of tests. Minimax sparse rates of convergence are obtained with exponential probability, under weak moment's assumptions and possible contamination of the dataset. These derive from general risk bounds of the following informal structure max (minimax rate in the i.i.d. setup, number of outliers/number of observations). In this result, the number of outliers may be as large as (number of data) x (minimax rate) without affecting the rates. As an example, minimax rates s log(ed /s)/N of recovery of s-sparse vectors in R-d holding with exponentially large probability, are deduced for median-of-means versions of the LASSO when the noise has q(0) moments for some q(0) > 2, the entries of the design matrix have C-0 log(ed) moments and the dataset is corrupted by up to C-1s log(ed/s) outliers. (C) 2018 Elsevier B. V. All rights reserved.

【 授权许可】

Free