Date/heure
1 juillet 2022
11:00 - 12:00
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Perrine Lacroix (Université Paris-Saclay)
Catégorie d'évènement Probabilités et Statistique
Résumé
In a high-dimensional context, a classical approach to estimate the unknown parameter in a Gaussian linear regression consists in minimizing the penalized least-squares criterion. To get an oracle inequality on the predictive risk, the model selection theory developed by L. Birgé and P. Massart (2001) gives some penalty shapes known up to multiplicative constants. First, controlling the prediction quality is not sufficient to limit the selection of inactive variables. Thus, under a simplified model, we propose a theoretical study of the FDR criterion onto the model selection procedure. A data-dependent heuristics is then implemented to calibrate one of the penalty constants allowing to avoid selecting inactive variables while maintaining a high prediction quality. Secondly, under the general model, we propose an algorithm that extends the slope heuristics principle to calibrate the last two constants while maintaining a reasonnable control of the predictive risk.