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Entropy-Based Concentration Inequalities for Dependent Variables

Liva Ralaivola 1 Massih-Reza Amini 2
1 QARMA - éQuipe AppRentissage et MultimediA [Marseille]
LIF - Laboratoire d'informatique Fondamentale de Marseille
Abstract : We provide new concentration inequalities for functions of dependent variables. The work extends that of Janson (2004), which proposes concentration inequalities using a combination of the Laplace transform and the idea of fractional graph coloring, as well as many works that derive concentration inequalities using the entropy method (see, e.g., (Boucheron et al., 2003)). We give inequalities for fractionally sub-additive and fractionally self-bounding functions. In the way, we prove a new Talagrand concentration inequality for fractionally sub-additive functions of dependent variables. The results allow us to envision the derivation of generalization bounds for various applications where dependent variables naturally appear, such as in bipartite ranking.
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Contributor : Massih-Reza Amini <>
Submitted on : Tuesday, December 1, 2015 - 8:45:27 PM
Last modification on : Monday, March 29, 2021 - 2:45:02 PM


  • HAL Id : hal-01211199, version 1



Liva Ralaivola, Massih-Reza Amini. Entropy-Based Concentration Inequalities for Dependent Variables. International Conference on Machine Learning, Jul 2015, Lille, France. ⟨hal-01211199⟩



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