Adaptive Estimation of the Optimal ROC Curve and a Bipartite Ranking Algorithm

In this paper, we propose an adaptive algorithm for bipartite ranking and prove its statistical performance in a stronger sense than the AUC criterion. Our procedure builds on the RankOver algorithm proposed in (Clémençon & Vayatis, 2008a). The algorithm outputs a piecewise constant scoring rule which is obtained by overlaying a finite collection of classifiers. Here, each of these classifiers is the empirical solution of a specific minimum-volume set (MV-set) estimation problem. The main novelty arises from the fact that the levels of the MV-sets to recover are chosen adaptively from the data to adjust to the variability of the target curve. The ROC curve of the estimated scoring rule may be interpreted as an adaptive spline approximant of the optimal ROC curve. Error bounds for the estimate of the optimal ROC curve in terms of the L∞-distance are also provided.