A Large Deviation Bound for the Area Under the ROC Curve

Part of Advances in Neural Information Processing Systems 17 (NIPS 2004)

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Shivani Agarwal, Thore Graepel, Ralf Herbrich, Dan Roth


The area under the ROC curve (AUC) has been advocated as an evalu- ation criterion for the bipartite ranking problem. We study large devi- ation properties of the AUC; in particular, we derive a distribution-free large deviation bound for the AUC which serves to bound the expected accuracy of a ranking function in terms of its empirical AUC on an inde- pendent test sequence. A comparison of our result with a corresponding large deviation result for the classification error rate suggests that the test sample size required to obtain an -accurate estimate of the expected ac- curacy of a ranking function with δ-confidence is larger than that required to obtain an -accurate estimate of the expected error rate of a classifi- cation function with the same confidence. A simple application of the union bound allows the large deviation bound to be extended to learned ranking functions chosen from finite function classes.