Overlaying classifiers: a practical approach for optimal ranking

ROC curves are one of the most widely used displays to evaluate performance of scoring functions. In the paper, we propose a statistical method for directly optimizing the ROC curve. The target is known to be the regression function up to an increasing transformation and this boils down to recovering the level sets of the latter. We propose to use classifiers obtained by empirical risk minimization of a weighted classification error and then to construct a scoring rule by overlaying these classifiers. We show the consistency and rate of convergence to the optimal ROC curve of this procedure in terms of supremum norm and also, as a byproduct of the analysis, we derive an empirical estimate of the optimal ROC curve.