{"id":148426,"date":"2005-01-01T00:00:00","date_gmt":"2005-01-01T00:00:00","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/msr-research-item\/generalization-error-bounds-for-the-area-under-the-roc-curve\/"},"modified":"2018-10-16T20:01:59","modified_gmt":"2018-10-17T03:01:59","slug":"generalization-error-bounds-for-the-area-under-the-roc-curve","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/generalization-error-bounds-for-the-area-under-the-roc-curve\/","title":{"rendered":"Generalization Error Bounds for the Area Under the ROC curve"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We study generalization properties of the area under the ROC curve (AUC), a quantity that has been advocated as an evaluation criterion for the bipartite ranking problem. The AUC is a different term than the error rate used for evaluation in classification problems; consequently, existing generalization bounds for the classification error rate cannot be used to draw conclusions about the AUC. In this paper, we define the expected accuracy of a ranking function (analogous to the expected error rate of a classification function), and derive distribution-free probabilistic bounds on the deviation of the empirical AUC of a ranking function (observed on a finite data sequence) from its expected accuracy. We derive both a large deviation bound, which serves to bound the expected accuracy of a ranking function in terms of its empirical AUC on a test sequence, and a uniform convergence bound, which serves to bound the expected accuracy of a learned ranking function in terms of its empirical AUC on a training sequence. Our uniform convergence 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. (2003) for a quantity closely related to the AUC shows that the bound provided by our result can be considerably tighter.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study generalization properties of the area under the ROC curve (AUC), a quantity that has been advocated as an evaluation criterion for the bipartite ranking problem. The AUC is a different term than the error rate used for evaluation in classification problems; consequently, existing generalization bounds for the classification error rate cannot be used [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"MIT Press","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Journal of Machine Learning Research","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Journal of Machine Learning 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