Variable selection through CART

Marie Sauvé (1) , Christine Tuleau-Malot (2)

1 Lycée d'Orléans
2 JAD - Laboratoire Jean Alexandre Dieudonné

This paper deals with variable selection in the regression and binary classification frameworks. It proposes an automatic and exhaustive procedure which relies on the use of the CART algorithm and on model selection via penalization. This work, of theoretical nature, aims at determining adequate penalties, i.e. penalties which allow to get oracle type inequalities justifying the performance of the proposed procedure. Since the exhaustive procedure can not be executed when the number of variables is too large, a more practical procedure is also proposed and still theoretically validated. A simulation study completes the theoretical results.

Mots clés: Binary classification; CART; Model selection; Penalization; Regression; Variable selection

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Marie Sauvé, Christine Tuleau-Malot. Variable selection through CART. ESAIM: Probability and Statistics, 2014, 18, pp.770-798. ⟨10.1051/ps/2014006⟩. ⟨hal-00551375v1⟩