Chromatic PAC-Bayes Bounds for Non-IID Data

Pac-Bayes bounds are among the most accurate generalization bounds for classifiers learned with \iid data, and it is particularly so for margin classifiers. However, there are many practical cases where the training data show some dependencies and where the traditional \iid assumption does not apply. Stating generalization bound for such frameworks is therefore of the utmost interest. In this work, we propose the first, to the best of our knowledge, \pac-Bayes generalization bounds for classifiers trained on data exhibiting dependencies. The approach is based on the decomposition of a so-called dependency graph of the data in sets of independent data, through the tool of fractional covers. Our bounds are very general, since being able to find an upper bound on the chromatic number of the dependency graph is sufficient for it get new bounds for specific settings. We show how our results can be used to derive bounds for bipartite ranking and windowed prediction.