Machine Learning

, Volume 107, Issue 5, pp 887–902 | Cite as

Simpler PAC-Bayesian bounds for hostile data

  • Pierre Alquier
  • Benjamin Guedj


PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to connect the generalization ability of an aggregation distribution \(\rho \) to its empirical risk and to its Kullback-Leibler divergence with respect to some prior distribution \(\pi \). Unfortunately, most of the available bounds typically rely on heavy assumptions such as boundedness and independence of the observations. This paper aims at relaxing these constraints and provides PAC-Bayesian learning bounds that hold for dependent, heavy-tailed observations (hereafter referred to as hostile data). In these bounds the Kullack-Leibler divergence is replaced with a general version of Csiszár’s f-divergence. We prove a general PAC-Bayesian bound, and show how to use it in various hostile settings.


PAC-Bayesian theory Dependent and unbounded data Oracle inequalities f-divergence 



We would like to thank Pascal Germain for fruitful discussions, along with two anonymous Referees and the Editor for insightful comments.This author gratefully acknowledges financial support from the research programme New Challenges for New Data from LCL and GENES, hosted by the Fondation du Risque, from Labex ECODEC (ANR-11-LABEX-0047) and from Labex CEMPI (ANR-11-LABX-0007-01).


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.CREST, ENSAE, Université Paris SaclayParisFrance
  2. 2.Modal Project-Team, InriaLille - Nord Europe research centerFrance

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