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Journal Articles Machine Learning Year : 2018

Simpler PAC-Bayesian Bounds for Hostile Data


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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Dates and versions

hal-01385064 , version 1 (20-10-2016)
hal-01385064 , version 2 (23-10-2016)
hal-01385064 , version 3 (23-05-2019)



Pierre Alquier, Benjamin Guedj. Simpler PAC-Bayesian Bounds for Hostile Data. Machine Learning, 2018, 107 (5), pp.887-902. ⟨10.1007/s10994-017-5690-0⟩. ⟨hal-01385064v3⟩
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