A Large Deviation Bound for the Area Under the ROC Curve

Shivani Agarwal, Thore Graepel, Ralf Herbrich, and Dan Roth

January 2004

The area under the ROC curve (AUC) has been advocated as an evaluation criterion for the bipartite ranking problem. We study large deviation 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 independent 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 epsilon-accurate estimate of the expected accuracy of a ranking function with delta-confidence is larger than that required to obtain an epsilon-accurate estimate of the expected error rate of a classification 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.

Publication type | Inproceedings |

Published in | Advances in Neural Information Processing Systems 17 |

Pages | 9-16 |

Publisher | MIT Press All copyrights reserved by MIT Press 2004. |

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