Non-asymptotic oracle inequalities for the Lasso and Group Lasso in high dimensional logistic model

¹ Laboratoire de Mathématique et modélisation d’Evry UMR CNRS 8071- USC INRA, Université d’Évry Val d’Essonne, Evry, France.
marius.kwemou@gmail.com
² LERSTAD, Université Gaston Berger de Saint-Louis, Sénégal.

Received: 1 July 2014
Revised: 25 November 2015
Accepted: 4 December 2015

Abstract

We consider the problem of estimating a function f₀ in logistic regression model. We propose to estimate this function f₀ by a sparse approximation build as a linear combination of elements of a given dictionary of p functions. This sparse approximation is selected by the Lasso or Group Lasso procedure. In this context, we state non asymptotic oracle inequalities for Lasso and Group Lasso under restricted eigenvalue assumption as introduced in [P.J. Bickel, Y. Ritov and A.B. Tsybakov, Ann. Statist. 37 (2009) 1705–1732].