Model selection in logistic regression

TL;DR

This paper extends the model selection principle to logistic regression using penalized likelihood and introduces a data-driven criterion based on slope heuristics, with theoretical guarantees and simulation validation.

Contribution

It adapts the model selection principle to logistic regression and proposes a novel data-driven criterion based on slope heuristics with proven theoretical properties.

Findings

Non-asymptotic oracle inequalities established

Simulation studies validate the theoretical results

Method effectively selects models in logistic regression

Abstract

This paper is devoted to model selection in logistic regression. We extend the model selection principle introduced by Birg\'e and Massart (2001) to logistic regression model. This selection is done by using penalized maximum likelihood criteria. We propose in this context a completely data-driven criteria based on the slope heuristics. We prove non asymptotic oracle inequalities for selected estimators. Theoretical results are illustrated through simulation studies.