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The ROC curve is the gold standard for measuring the performance of atest/scoring statistic regarding its capacity to discriminate between twostatistical populations in a wide variety of applications, ranging from anomalydetection in signal processing to information retrieval, through medicaldiagnosis. Most practical performance measures used in scoring/rankingapplications such as the AUC, the local AUC, the p-norm push, the DCG andothers, can be viewed as summaries of the ROC curve. In this paper, the factthat most of these empirical criteria can be expressed as two-sample linearrank statistics is highlighted and concentration inequalities for collectionsof such random variables, referred to as two-sample rank processes here, areproved, when indexed by VC classes of scoring functions. Based on thesenonasymptotic bounds, the generalization capacity of empirical maximizers of awide class of ranking performance criteria is next investigated from atheoretical perspective. It is also supported by empirical evidence throughconvincing numerical experiments.

Concentration Inequalities for Two-Sample Rank Processes with Application to Bipartite Ranking