Abstract
In this chapter, we introduce the statistical ranking framework. In order to analyze the theoretical properties of learning-to-rank methods, the very first step is to establish the right probabilistic context for the analysis. This is just what the statistical ranking framework addresses. In this chapter we will show three ranking frameworks used in the literature of learning to rank, i.e., the document ranking framework, the subset ranking framework, and the two-layer ranking framework. The discussions in this chapter set the stage for further discussions on generalization ability and statistical consistency in the following chapters.
References
Agarwal, S.: Generalization bounds for some ordinal regression algorithms. In: Proceedings of the 19th International Conference on Algorithmic Learning Theory (ALT 2008), pp. 7–21 (2008)
Agarwal, S., Graepel, T., Herbrich, R., Har-Peled, S., Roth, D.: Generalization bounds for the area under the roc curve. Journal of Machine Learning 6, 393–425 (2005)
Agarwal, S., Niyogi, P.: Stability and generalization of bipartite ranking algorithms. In: Proceedings of the 18th Annual Conference on Learning Theory (COLT 2005), pp. 32–47 (2005)
Chen, W., Liu, T.Y., Ma, Z.M.: Two-layer generalization analysis for ranking using rademacher average. In: Lafferty, J., Williams, C.K.I., Shawe-Taylor, J., Zemel, R., Culotta, A. (eds.) Advances in Neural Information Processing Systems 23 (NIPS 2010), pp. 370–378 (2011)
Clemencon, S., Lugosi, G., Vayatis, N.: Ranking and empirical minimization of U-statistics. The Annals of Statistics 36(2), 844–874 (2008)
Cossock, D., Zhang, T.: Subset ranking using regression. In: Proceedings of the 19th Annual Conference on Learning Theory (COLT 2006), pp. 605–619 (2006)
Freund, Y., Iyer, R., Schapire, R., Singer, Y.: An efficient boosting algorithm for combining preferences. Journal of Machine Learning Research 4, 933–969 (2003)
Lan, Y., Liu, T.Y.: Generalization analysis of listwise learning-to-rank algorithms. In: Proceedings of the 26th International Conference on Machine Learning (ICML 2009), pp. 577–584 (2009)
Lan, Y., Liu, T.Y., Qin, T., Ma, Z., Li, H.: Query-level stability and generalization in learning to rank. In: Proceedings of the 25th International Conference on Machine Learning (ICML 2008), pp. 512–519 (2008)
Rajaram, S., Agarwal, S.: Generalization bounds for k-partite ranking. In: NIPS 2005 Workshop on Learning to Rank (2005)
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Liu, TY. (2011). Statistical Ranking Framework. In: Learning to Rank for Information Retrieval. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14267-3_16
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DOI: https://doi.org/10.1007/978-3-642-14267-3_16
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