Monotone Instance Ranking with mira

  • Nicola Barile
  • Ad Feelders
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6926)


In many ranking problems, common sense dictates that the rank assigned to an instance should be increasing (or decreasing) in one or more of the attributes describing it. Consider, for example, the problem of ranking documents with respect to their relevance to a particular query. Typical attributes are counts of query terms in the abstract or title of the document, so it is natural to postulate the existence of an increasing relationship between these counts and document relevance. Such relations between attributes and rank are called monotone. In this paper we present a new algorithm for instance ranking called mira which learns a monotone ranking function from a set of labelled training examples. Monotonicity is enforced by applying the isotonic regression to the training sample, together with an interpolation scheme to rank new data points. This is combined with logistic regression in an attempt to remove unwanted rank equalities. Through experiments we show that mira produces ranking functions having predictive performance comparable to that of a state-of-the-art instance ranking algorithm. This makes mira a valuable alternative when monotonicity is desired or mandatory.


Class Label Ranking Function Attribute Vector Query Term Aggregation Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
  2. 2.
  3. 3.
  4. 4.
    Altendorf, E.A., Restificar, A.C., Dietterich, T.G.: Learning from sparse data by exploiting monotonicity constraints. In: Bacchus, F., Jaakkola, T. (eds.) Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence (UAI 2005), pp. 18–25. AUAI Press (2005)Google Scholar
  5. 5.
    Anglin, P.M., Gençay, R.: Semiparametric estimation of a hedonic price function. Journal of Applied Econometrics 11, 633–648 (1996)CrossRefGoogle Scholar
  6. 6.
    Asuncion, A., Newman, D.J.: UCI machine learning repository (2007)Google Scholar
  7. 7.
    Barile, N., Feelders, A.: Nonparametric monotone classification with MOCA. In: Giannotti, F. (ed.) Proceedings of the Eighth IEEE International Conference on Data Mining (ICDM 2008), pp. 731–736. IEEE Computer Society, Los Alamitos (2008)Google Scholar
  8. 8.
    Barile, N., Feelders, A.: Nonparametric ordinal classification with monotonicity constraints. In: Feelders, A., Potharst, R. (eds.) Workshop Proceedings of MoMo 2009 at ECML PKDD 2009, pp. 47–63 (2009)Google Scholar
  9. 9.
    Ben-David, A.: Monotonicity maintenance in information-theoretic machine learning algorithms. Machine Learning 19, 29–43 (1995)Google Scholar
  10. 10.
    Burdakov, O., Sysoev, O., Grimvall, A., Hussian, M.: An O(n 2) algorithm for isotonic regression. In: Di Pillo, G., Roma, M. (eds.) Large-Scale Nonlinear Optimization, pp. 25–33. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Dembczynski, K., Kotlowski, W., Slowinski, R.: Ordinal classification with decision rules. In: Raś, Z.W., Tsumoto, S., Zighed, D. (eds.) Proceedings of the 3rd ECML/PKDD International Conference on Mining Complex Data, Warsaw, Poland, pp. 169–181. Springer, Heidelberg (2007)Google Scholar
  12. 12.
    Demšar, J.: Statistical comparisons of classifiers over multiple data sets. The Journal of Machine Learning Research 7, 1–30 (2006)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Druzdzel, M.J., van der Gaag, L.C.: Elicitation of probabilities for belief networks: Combining qualitative and quantitative information. In: Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence (UAI 1995), Los Altos CA, pp. 141–148. Morgan Kaufmann, San Francisco (1995)Google Scholar
  14. 14.
    Feelders, A., van der Gaag, L.: Learning Bayesian network parameters with prior knowledge about context-specific qualitative influences. In: Bacchus, F., Jaakkola, T. (eds.) Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence (UAI 2005), pp. 193–200. AUAI Press (2005)Google Scholar
  15. 15.
    Frank, E., Hall, M.: A simple approach to ordinal classification. In: De Raedt, L., Flach, P.A. (eds.) Proceedings of the 12th European Conference on Machine Learning (ECML/PKDD 2001), Freiburg, Germany, pp. 145–156. Springer, Heidelberg (2001)Google Scholar
  16. 16.
    Fürnkranz, J., Hüllermeier, E.: Preference Learning. Springer, Heidelberg (2010)zbMATHGoogle Scholar
  17. 17.
    Fürnkranz, J., Hüllermeier, E., Vanderlooy, S.: Binary decomposition methods for multipartite ranking. In: Buntine, W.L., Grobelnik, M., Mladenic, D., Shawe-Taylor, J. (eds.) Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML/PKDD 2009), Bled, Slovenia, vol. Part I, pp. 359–374. Springer, Heidelberg (2009)Google Scholar
  18. 18.
    Gönen, M., Heller, G.: Concordance probability and discriminatory power in proportional hazards regression. Biometrika 92(4), 965–970 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Herbrich, R., Graepel, T., Obermayer, K.: Large margin rank boundaries for ordinal regression. Advances in Large-Margin Classifiers, 115–132 (2000)Google Scholar
  20. 20.
    Lievens, S., De Baets, B., Cao-Van, K.: A probabilistic framework for the design of instance-based supervised ranking algorithms in an ordinal setting. Annals of Operations Research 163, 115–142 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Meyer, M.A., Booker, J.M.: Eliciting and Analyzing Expert Judgment: A Practical Guide. Series on Statistics and Applied Probability. ASA-SIAM (2001)Google Scholar
  22. 22.
    Pazzani, M.J., Mani, S., Shankle, W.R.: Acceptance of rules generated by machine learning among medical experts. Methods of Information in Medicine 40, 380–385 (2001)Google Scholar
  23. 23.
    Potharst, R., Bioch, J.C.: Decision trees for ordinal classification. Intelligent Data Analysis 4(2), 97–112 (2000)zbMATHGoogle Scholar
  24. 24.
    Sill, J.: Monotonic networks. In: Advances in Neural Information Processing Systems, NIPS, vol. 10, pp. 661–667 (1998)Google Scholar
  25. 25.
    Spouge, J., Wan, H., Wilbur, W.J.: Least squares isotonic regression in two dimensions. Journal of Optimization Theory and Applications 117(3), 585–605 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    van de Kamp, R., Feelders, A., Barile, N.: Isotonic classification trees. In: Adams, N., Robardet, C., Siebes, A., Boulicaut, J.-F. (eds.) Proceedings of the 8th International Symposium on Intelligent Data Analysis: Advances in Intelligent Data Analysis VIII, Lyon, France, pp. 405–416. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nicola Barile
    • 1
  • Ad Feelders
    • 1
  1. 1.Department of Information and Computing SciencesUniversiteit UtrechtUtrechtThe Netherlands

Personalised recommendations