Weak transport inequalities and applications to exponential and oracle inequalities.

Olivier Wintenberger (Université Paris Dauphine, CREST)
vendredi 15 février 2013

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).