Simpler PAC-Bayesian Bounds for Hostile Data

Pierre Alquier 1, 2 Benjamin Guedj 3
3 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, CERIM - Santé publique : épidémiologie et qualité des soins-EA 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : 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 \emph{hostile data}). In these bounds the Kullack-Leibler divergence is replaced with a general version of Csisz\'ar's $f$-divergence. We prove a general PAC-Bayesian bound, and show how to use it in various hostile settings.
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Submitted on : Thursday, May 23, 2019 - 7:57:05 AM
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Pierre Alquier, Benjamin Guedj. Simpler PAC-Bayesian Bounds for Hostile Data. Machine Learning, Springer Verlag, 2018, 107 (5), pp.887-902. ⟨10.1007/s10994-017-5690-0⟩. ⟨hal-01385064v3⟩



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