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