  Pac-Bayes bounds are among the most accurate generalization bounds for
classifiers learned from independently and identically distributed (IID) data,
and it is particularly so for margin classifiers: there have been recent
contributions showing how practical these bounds can be either to perform model
selection (Ambroladze et al., 2007) or even to directly guide the learning of
linear classifiers (Germain et al., 2009). However, there are many practical
situations where the training data show some dependencies and where the
traditional IID assumption does not hold. Stating generalization bounds for
such frameworks is therefore of the utmost interest, both from theoretical and
practical standpoints. In this work, we propose the first - to the best of our
knowledge - Pac-Bayes generalization bounds for classifiers trained on data
exhibiting interdependencies. The approach undertaken to establish our results
is based on the decomposition of a so-called dependency graph that encodes the
dependencies within the data, in sets of independent data, thanks to graph
fractional covers. Our bounds are very general, since being able to find an
upper bound on the fractional chromatic number of the dependency graph is
sufficient to get new Pac-Bayes bounds for specific settings. We show how our
results can be used to derive bounds for ranking statistics (such as Auc) and
classifiers trained on data distributed according to a stationary {\ss}-mixing
process. In the way, we show how our approach seemlessly allows us to deal with
U-processes. As a side note, we also provide a Pac-Bayes generalization bound
for classifiers learned on data from stationary $\varphi$-mixing distributions.
