Simultaneous adaptation to the margin and to complexity in classification

Guillaume Lecué (1, 2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We consider the problem of adaptation to the margin and to complexity in binary classification. We suggest a learning method with a numerically easy aggregation step. Adaptivity both to the margin and complexity in classification, usually involves empirical risk minimization or Rademacher complexities which lead to numerical difficulties. On the other hand there exist classifiers that are easy to compute and that converge with fast rates but are not adaptive. Combining these classifiers by our aggregation procedure we get numerically realizable adaptive classifiers that converge with fast rates.

Mots clés: Classification; statistical learning; aggregation of classi- fiers; optimal rates; margin; complexity of classes of sets; SVM.; SVM

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

Guillaume Lecué. Simultaneous adaptation to the margin and to complexity in classification. 2006. ⟨hal-00009241v2⟩