On partitioning rules for bipartite ranking

The purpose of this paper is to investigate the properties of partitioning scoring rules in the bipartite ranking setup. We focus on ranking rules based on scoring functions. General sufficient conditions for the AUC consistency of scoring functions that are constant on cells of a partition of the feature space are provided. Rate bounds are obtained for cubic histogram scoring rules under mild smoothness assumptions on the regression function. In this setup, it is shown how to penalize the empirical AUC criterion in order to select a scoring rule nearly as good as the one that can be built when the degree of smoothness of the regression function is known.