Generalization Bounds of Ranking via Query-Level Stability I

  • Xiangguang He
  • Wei Gao
  • Zhiyang Jia
Part of the Communications in Computer and Information Science book series (CCIS, volume 236)


The quality of ranking determines the success or failure of information retrieval and the goal of ranking is to learn a real-valued ranking function that induces a ranking or ordering over an instance space. We focus on generalization ability of learning to rank algorithms for information retrieval (IR). The contribution of this paper is to give generalization bounds for such ranking algorithm via uniform (strong and weak) query-level stability by deleting one element from sample set or change one element in sample set. Only we define the corresponding definitions and list all the lemmas we need. All results will show in “Generalization Bounds of Ranking via Query-Level Stability II”.


ranking algorithmic stability generalization bounds strong stability weak stability 


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  1. 1.
    Cynthia, R., Robert, E., Ingrid, D.: Boosting based on a smooth margin. In: Proceedings of the 16th Annual Conference on Computational Learning Theory, pp. 502–517 (2004)Google Scholar
  2. 2.
    Burges, C.: Learning to rank using gradient descent. In: Proceedings of the 22nd Intl Conference on Machine Learning, pp. 89–96 (2005)Google Scholar
  3. 3.
    Rong, Y., Alexander, Hauptmann, D.: Efficient margin-based rank learning algorithms for information retrieval. In: Sundaram, H., Naphade, M., Smith, J.R., Rui, Y. (eds.) CIVR 2006. LNCS, vol. 4071, pp. 113–122. Springer, Heidelberg (2006)Google Scholar
  4. 4.
    Cynthia, R.: Ranking with a P-Norm Push. In: Lugosi, G., Simon, H.U. (eds.) COLT 2006. LNCS (LNAI), vol. 4005, pp. 589–604. Springer, Heidelberg (2006)Google Scholar
  5. 5.
    Joachims, T.: Optimizing search engines using clickthrough data. In: Proc.The 8th ACM SIGKDD Intl Conference on Knowledge Discovery and Data Mining, pp. 133–142. ACM Press, New York (2002)Google Scholar
  6. 6.
    Chua, T.S., Neo, S.Y., Goh, H.K., et al.: Trecvid 2005 by nus pris. NIST TRECVID (2005)Google Scholar
  7. 7.
    Corinna, C., Mehryar, M., Ashish, R.: Magnitude-Preserving Ranking Algorithms. In: Proc. The 24th International Conference on Machine Learning. OR, Corvallis (2007)Google Scholar
  8. 8.
    Kutin, S., Niyogi, P.: The interaction of stability and weakness in AdaBoost, Technical Report TR-2001-30, Computer Science Department, University of Chicago (2001)Google Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    Garwal, Niyogi, P.: Generalization bounds for ranking algorithms via algorithmic stability. Journal of Machine Learning Research 10, 441–474 (2009)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Cynthia, R.: The P-Norm Push: A simple convex ranking algorithm that concentrates at the top of the list. Journal of Machine Learning Research 10, 2233–2271 (2009)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Gao, W., Zhang, Y., Liang, L., Xia, Y.: Stability analysis for ranking algorithms. In: IEEE International Conference on Information Theory and Information Security (ICITIS), Beijing, pp. 973–976 (December 2010)Google Scholar
  13. 13.
    Lan, Y., Liu, T., Qin, T., Ma, Z., Li, H.: Query-Level Stability and Generalization in Learning to Rank, Appearing. In: Proceedings of the 25 th International Conference on Machine Learning, Helsinki, Finland (2008)Google Scholar
  14. 14.
    Kutin, S., Niyogi, P.: Almost-everywhere algorithmic stability and generalization error. In: Proceedings of the 18th Conference on Uncertainty in Artificial Intelligence (2002)Google Scholar
  15. 15.
    McDiarmid, C.: On the method of bounded differences. In: Surveys in Combinatorics 1989, pp. 148–188. Cambridge University Press, Cambridge (1989)Google Scholar
  16. 16.
    Kutin, S.: Extensions to McDiarmid’s inequality when differences are bounded with high probability, Technical report, Department of Computer Science, The university of Chicago (2002)Google Scholar
  17. 17.
    Rakhlin, A., Mukherjee, S., Poggio, T.: Stability results in learning theory. Analysis and Applications 3, 397–417 (2005)MathSciNetzbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Xiangguang He
    • 1
  • Wei Gao
    • 2
    • 3
  • Zhiyang Jia
    • 4
  1. 1.Department of Information EngineeringBinzhou PolytechnicBinzhouChina
  2. 2.Department of InformationYunnan Normal UniversityKunmingChina
  3. 3.Department of MathematicsSoochow UniversitySuzhouChina
  4. 4.Department of InformationTourism and Literature college of Yunnan UniversityLijiangChina

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