### Abstract

The area under the ROC curve (AUC) has been advocated as an evaluation criterion for the bipartite ranking problem. We study uniform convergence properties of the AUC; in particular, we derive a distribution-free uniform convergence bound for the AUC which serves to bound the expected accuracy of a learned ranking function in terms of its empirical AUC on the training sequence from which it is learned. Our bound is expressed in terms of a new set of combinatorial parameters that we term the bipartite rank-shatter coefficients; these play the same role in our result as do the standard VC-dimension related shatter coefficients (also known as the growth function) in uniform convergence results for the classification error rate. A comparison of our result with a recent uniform convergence result derived by Freund et al. [9] for a quantity closely related to the AUC shows that the bound provided by our result can be considerably tighter.

Original language | English (US) |
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Title of host publication | AISTATS 2005 - Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics |

Pages | 1-8 |

Number of pages | 8 |

State | Published - Dec 1 2005 |

Event | 10th International Workshop on Artificial Intelligence and Statistics, AISTATS 2005 - Hastings, Christ Church, Barbados Duration: Jan 6 2005 → Jan 8 2005 |

### Publication series

Name | AISTATS 2005 - Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics |
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### Other

Other | 10th International Workshop on Artificial Intelligence and Statistics, AISTATS 2005 |
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Country | Barbados |

City | Hastings, Christ Church |

Period | 1/6/05 → 1/8/05 |

### ASJC Scopus subject areas

- Artificial Intelligence
- Statistics and Probability

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## Cite this

*AISTATS 2005 - Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics*(pp. 1-8). (AISTATS 2005 - Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics).