Skip to main content

Statistical Learning Theory for Ranking

  • Chapter
  • 4707 Accesses

Abstract

In this chapter, we introduce the statistical learning theory for ranking. In order to better understand existing learning-to-rank algorithms, and to design better algorithms, it is very helpful to deeply understand their theoretical properties. In this chapter, we give the big picture of theoretical analysis for ranking, and point out several important issues to be investigated: statistical ranking framework, generalization ability, and statistical consistency for ranking methods.

This is a preview of subscription content, log in via an institution.

References

  1. 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)

    Chapter  Google Scholar 

  2. 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)

    MathSciNet  Google Scholar 

  3. 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)

    Google Scholar 

  4. 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)

    Google Scholar 

  5. Clemencon, S., Lugosi, G., Vayatis, N.: Ranking and empirical minimization of u-statistics. The Annals of Statistics 36(2), 844–874 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cossock, D., Zhang, T.: Subset ranking using regression. In: Proceedings of the 19th Annual Conference on Learning Theory (COLT 2006), pp. 605–619 (2006)

    Google Scholar 

  7. Freund, Y., Iyer, R., Schapire, R., Singer, Y.: An efficient boosting algorithm for combining preferences. Journal of Machine Learning Research 4, 933–969 (2003)

    MathSciNet  Google Scholar 

  8. 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)

    Google Scholar 

  9. Lan, Y., Liu, T.Y., Ma, Z.M., Li, H.: Statistical consistency of ranking methods. Tech. rep., Microsoft Research (2010)

    Google Scholar 

  10. 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)

    Chapter  Google Scholar 

  11. Rajaram, S., Agarwal, S.: Generalization bounds for k-partite ranking. In: NIPS 2005 Workshop on Learning to Rank (2005)

    Google Scholar 

  12. Xia, F., Liu, T.Y., Li, H.: Statistical consistency of top-k ranking. In: Advances in Neural Information Processing Systems 22 (NIPS 2009), pp. 2098–2106 (2010)

    Google Scholar 

  13. Xia, F., Liu, T.Y., Wang, J., Zhang, W., Li, H.: Listwise approach to learning to rank—theorem and algorithm. In: Proceedings of the 25th International Conference on Machine Learning (ICML 2008), pp. 1192–1199 (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tie-Yan Liu .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Liu, TY. (2011). Statistical Learning Theory for Ranking. In: Learning to Rank for Information Retrieval. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14267-3_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14267-3_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14266-6

  • Online ISBN: 978-3-642-14267-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics