Weak transport inequalities and applications to exponential and oracle inequalities.
Résumé : We extend the weak transport as defined in Marton (1996) to other metrics than the Hamming distance. We obtain new weak transport inequalities for non product measures. Many examples are provided to show that the euclidian norm is an appropriate metric for many classical time series. The dual form of the weak transport inequalities yield new exponential inequalities and extensions to the dependent case of the classical result of Talagrand (1995) for convex functions that are Lipschitz continuous. Expressing the concentration properties of the ordinary least square estimator as a conditional weak transport problem, we derive from the weak transport inequalities new oracle inequalities with fast rates of convergence. We also provide a new aggregation procedure when multiple models are considered.
Cet exposé se tiendra en salle C20-13, 20ème étage, Université Paris 1, Centre Pierre Mendès-France, 90 rue de Tolbiac, 75013 Paris (métro : Olympiades).