#### Authors

Jean-yves Audibert, Olivier Bousquet

#### Abstract

There exist many different generalization error bounds for classiﬁcation. Each of these bounds contains an improvement over the others for cer- tain situations. Our goal is to combine these different improvements into a single bound. In particular we combine the PAC-Bayes approach intro- duced by McAllester [1], which is interesting for averaging classiﬁers, with the optimal union bound provided by the generic chaining technique developed by Fernique and Talagrand [2]. This combination is quite nat- ural since the generic chaining is based on the notion of majorizing mea- sures, which can be considered as priors on the set of classiﬁers, and such priors also arise in the PAC-bayesian setting.