Corinna Cortes, Mehryar Mohri
The area under an ROC curve (AUC) is a criterion used in many appli- cations to measure the quality of a classiﬁcation algorithm. However, the objective function optimized in most of these algorithms is the error rate and not the AUC value. We give a detailed statistical analysis of the relationship between the AUC and the error rate, including the ﬁrst exact expression of the expected value and the variance of the AUC for a ﬁxed error rate. Our results show that the average AUC is monotonically in- creasing as a function of the classiﬁcation accuracy, but that the standard deviation for uneven distributions and higher error rates is noticeable. Thus, algorithms designed to minimize the error rate may not lead to the best possible AUC values. We show that, under certain conditions, the global function optimized by the RankBoost algorithm is exactly the AUC. We report the results of our experiments with RankBoost in several datasets demonstrating the beneﬁts of an algorithm speciﬁcally designed to globally optimize the AUC over other existing algorithms optimizing an approximation of the AUC or only locally optimizing the AUC.