  The ROC curve is the gold standard for measuring the performance of a
test/scoring statistic regarding its capacity to discriminate between two
statistical populations in a wide variety of applications, ranging from anomaly
detection in signal processing to information retrieval, through medical
diagnosis. Most practical performance measures used in scoring/ranking
applications such as the AUC, the local AUC, the p-norm push, the DCG and
others, can be viewed as summaries of the ROC curve. In this paper, the fact
that most of these empirical criteria can be expressed as two-sample linear
rank statistics is highlighted and concentration inequalities for collections
of such random variables, referred to as two-sample rank processes here, are
proved, when indexed by VC classes of scoring functions. Based on these
nonasymptotic bounds, the generalization capacity of empirical maximizers of a
wide class of ranking performance criteria is next investigated from a
theoretical perspective. It is also supported by empirical evidence through
convincing numerical experiments.
