Non-asymptotic Oracle Inequalities for the Lasso and Group Lasso in high dimensional logistic model

TL;DR

This paper establishes non-asymptotic oracle inequalities for Lasso and Group Lasso estimators in high-dimensional logistic regression, providing theoretical guarantees for sparse function approximation.

Contribution

It introduces non-asymptotic oracle inequalities for Lasso and Group Lasso in high-dimensional logistic models under restricted eigenvalue conditions.

Findings

Oracle inequalities hold with high probability.

Results apply to sparse function approximation.

Theoretical guarantees under restricted eigenvalue assumptions.

Abstract

We consider the problem of estimating a function $f\_{0}$ in logistic regression model. We propose to estimate this function $f\_{0}$ 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 eigenvalues assumption as introduced in \cite{BRT}.