Abstract
We reduce ranking, as measured by the Area Under the Receiver Operating Characteristic Curve (AUC), to binary classification. The core theorem shows that a binary classification regret of r on the induced binary problem implies an AUC regret of at most 2r. This is a large improvement over approaches such as ordering according to regressed scores, which have a regret transform of r ↦nr where n is the number of elements.
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References
Agarwal, S., Har-Peled, S., Roth, D.: A uniform convergence bound for the area under the ROC curve. In: Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics (2005)
Agarwal, S., Niyogi, P.: Stability and generalization of bipartite ranking algorithms. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS (LNAI), vol. 3559, pp. 32–47. Springer, Heidelberg (2005)
Alon, N.: Ranking tournaments. SIAM Journal on Discrete Mathematics 20, 137–142 (2006)
Bansal, N., Coppersmith, D., Sorkin, G.B.: A winner–loser labeled tournament has at most twice as many outdegree misrankings as pair misrankings, IBM Research Report RC24107 (November 2006)
Clémençon, S., Lugosi, G., Vayatis, N.: Ranking and scoring using empirical risk minimization. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS (LNAI), vol. 3559, pp. 1–15. Springer, Heidelberg (2005)
Cohen, W., Schapire, R., Singer, Y.: Learning to order things. Journal of Artificial Intelligence Research 10, 243–270 (1999)
Coppersmith, D., Fleischer, L., Rudra, A.: Ordering by weighted number of wins gives a good ranking for weighted tournaments. In: Proceeding of the 17th Annual Symposium on Discrete Algorithms (SODA), pp. 776–782 (2006)
Cortes, C., Mohri, M.: AUC optimization versus error rate minimization, Advances in Neural Information Processing Systems (NIPS) (2004)
Freund, Y., Iyer, R., Schapire, R., Singer, Y.: An efficient boosting algorithm for combining preferences. J. of Machine Learning Research 4, 933–969 (2003)
Landau, H.: On dominance relations and the structure of animal societies: III. The condition for a score structure. Bull. Math. Biophys. 15, 143–148 (1953)
Rudin, C., Cortes, C., Mohri, M., Schapire, R.: Margin-based ranking meets Boosting in the middle. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS (LNAI), vol. 3559, Springer, Heidelberg (2005)
Slater, P.: Inconsistencies in a schedule of paired comparisons. Biometrika 48, 303–312 (1961)
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Balcan, MF., Bansal, N., Beygelzimer, A., Coppersmith, D., Langford, J., Sorkin, G.B. (2007). Robust Reductions from Ranking to Classification. In: Bshouty, N.H., Gentile, C. (eds) Learning Theory. COLT 2007. Lecture Notes in Computer Science(), vol 4539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72927-3_43
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DOI: https://doi.org/10.1007/978-3-540-72927-3_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72925-9
Online ISBN: 978-3-540-72927-3
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