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Pré-Publication, Document De Travail Année : 2012

Weak transport inequalities and applications to exponential inequalities and oracle inequalities

Résumé

We introduce weak transport costs that are weakened forms of the transport costs defined by Marton in \cite{marton:1996a}. We obtain new weak transport inequalities for non products measures similar than those obtained by Samson in \cite{samson:2000} but valid also for other metrics than the Hamming distance. 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 \cite{talagrand:1995} for convex functions that are Lipschitz continuous. Expressing the concentration properties of the ordinary least square estimator as a conditional mass transport problem, we derive from the weak transport inequalities new oracle inequalities with fast rates of convergence.
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Dates et versions

hal-00719729 , version 1 (20-07-2012)
hal-00719729 , version 2 (08-11-2012)
hal-00719729 , version 3 (05-03-2014)

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Olivier Wintenberger. Weak transport inequalities and applications to exponential inequalities and oracle inequalities. 2012. ⟨hal-00719729v1⟩
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