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An estimation of generalized bradley-terry models based on the em algorithm.

Yu Fujimoto1, Hideitsu Hino, Noboru Murata

  • 1Department of Integrated Information Technology, Aoyama Gakuin University, Chuo, Sagamihara, Kanagawa 252-5258, Japan. yu.fujimoto@it.aoyama.ac.jp

Neural Computation
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Summary

This study introduces a new method for estimating the Bradley-Terry model using information geometry and the EM algorithm. The novel approach improves accuracy, especially with weight adaptation, for preference and ranking data.

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Area of Science:

  • Statistics
  • Information Geometry
  • Machine Learning

Background:

  • The Bradley-Terry model is a statistical tool for analyzing preference and ranking data derived from pairwise comparisons.
  • Existing estimation methods often rely on minimizing weighted Kullback-Leibler divergences.

Purpose of the Study:

  • To interpret Bradley-Terry model estimation through the lens of information geometry's 'flatness' concept.
  • To propose a novel estimation method for the Bradley-Terry model.
  • To introduce a weight adaptation technique for enhanced estimation sensitivity.

Main Methods:

  • Developed a new estimation method for the Bradley-Terry model within the Expectation-Maximization (EM) algorithm framework.
  • The proposed method utilizes a distinct objective function, particularly in handling unobserved comparisons.
  • Incorporated a weight adaptation strategy based on sensitivity analysis.

Main Results:

  • Experimental results validate the effectiveness of the proposed estimation method.
  • The weight adaptation technique demonstrably improves the accuracy of Bradley-Terry model estimates.
  • The new method offers a consistent interpretation within a probability simplex.

Conclusions:

  • The proposed information geometry-based EM algorithm provides a robust approach to Bradley-Terry model estimation.
  • Weight adaptation is a key factor in enhancing estimation accuracy for preference and ranking data.
  • This work offers a novel perspective on statistical model estimation through geometric principles.