Electronic Journal of Probability

Weak transport inequalities and applications to exponential and oracle inequalities

Olivier Wintenberger

Full-text: Open access

Abstract

We extend the dimension free Talagrand inequalities for convex distance using an extension of Marton’s weak transport to other metrics than the Hamming distance. We study the dual form of these weak transport inequalities for the euclidian norm and prove that it implies sub-gaussianity and convex Poincaré inequality. We obtain new weak transport inequalities for non products measures extending the results of Samson. Many examples are provided to show that the euclidian norm is an appropriate metric for classical time series. Our approach, based on trajectories coupling, is more efficient to obtain dimension free concentration than existing contractive assumptions. Expressing the concentration properties of the ordinary least square estimator as a conditional weak transport problem, we derive new oracle inequalities with fast rates of convergence in dependent settings.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 114, 27 pp.

Dates
Accepted: 29 October 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067220

Digital Object Identifier
doi:10.1214/EJP.v20-3558

Mathematical Reviews number (MathSciNet)
MR3418546

Zentralblatt MATH identifier
1328.60057

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Wintenberger, Olivier. Weak transport inequalities and applications to exponential and oracle inequalities. Electron. J. Probab. 20 (2015), paper no. 114, 27 pp. doi:10.1214/EJP.v20-3558. https://projecteuclid.org/euclid.ejp/1465067220


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