A Simple Lexicographic Ranker and Probability Estimator

  • Peter Flach
  • Edson Takashi Matsubara
Conference paper

DOI: 10.1007/978-3-540-74958-5_55

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4701)
Cite this paper as:
Flach P., Matsubara E.T. (2007) A Simple Lexicographic Ranker and Probability Estimator. In: Kok J.N., Koronacki J., Mantaras R.L.., Matwin S., Mladenič D., Skowron A. (eds) Machine Learning: ECML 2007. ECML 2007. Lecture Notes in Computer Science, vol 4701. Springer, Berlin, Heidelberg


Given a binary classification task, a ranker sorts a set of instances from highest to lowest expectation that the instance is positive. We propose a lexicographic ranker, LexRank, whose rankings are derived not from scores, but from a simple ranking of attribute values obtained from the training data. When using the odds ratio to rank the attribute values we obtain a restricted version of the naive Bayes ranker. We systematically develop the relationships and differences between classification, ranking, and probability estimation, which leads to a novel connection between the Brier score and ROC curves. Combining LexRank with isotonic regression, which derives probability estimates from the ROC convex hull, results in the lexicographic probability estimator LexProb. Both LexRank and LexProb are empirically evaluated on a range of data sets, and shown to be highly effective.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Peter Flach
    • 1
  • Edson Takashi Matsubara
    • 2
  1. 1.Department of Computer Science, University of BristolUnited Kingdom
  2. 2.Instituto de Ciências e Matemáticas e de Computação, Universidade de São Paulo 

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