Abstract
The Bradley-Terry model for obtaining individual skill from paired comparisons has been popular in many areas. In machine learning, this model is related to multi-class probability estimates by coupling all pairwise classification results. Error correcting output codes (ECOC) are a general framework to decompose a multi-class problem to several binary problems. To obtain probability estimates under this framework, this paper introduces a generalized Bradley-Terry model in which paired individual comparisons are extended to paired team comparisons. We propose a simple algorithm with convergence proofs to solve the model and obtain individual skill. Experiments on synthetic and re al data demonstrate that the algorithm is useful for obtaining multi-class probability estimates. Moreover, we discuss four extensions of the proposed model: 1) weighted individual skill, 2) home-field advantage, 3) ties, and 4) comparisons with more than two teams.
Keywords
Class (philosophy)Pairwise comparisonComputer scienceMathematical proofConvergence (economics)Binary numberArtificial intelligenceSimple (philosophy)Machine learningField (mathematics)AlgorithmTheoretical computer scienceMathematics
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Publication Info
- Year
- 2006
- Type
- article
- Volume
- 7
- Issue
- 4
- Pages
- 85-115
- Citations
- 151
- Access
- Closed
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Cite This
Tzu-Kuo Huang,
Ruby C. Weng,
Chih‐Jen Lin
(2006).
Generalized Bradley-Terry Models and Multi-Class Probability Estimates.
Journal of Machine Learning Research
, 7
(4)
, 85-115.
https://doi.org/10.5555/1248547.1248551
Identifiers
- DOI
- 10.5555/1248547.1248551