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6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

June 2011, Vol. 23, No. 6, Pages 1623-1659
(doi: 10.1162/NECO_a_00129)
© 2011 Massachusetts Institute of Technology
An Estimation of Generalized Bradley-Terry Models Based on the em Algorithm
Article PDF (971.66 KB)
Abstract

The Bradley-Terry model is a statistical representation for one's preference or ranking data by using pairwise comparison results of items. For estimation of the model, several methods based on the sum of weighted Kullback-Leibler divergences have been proposed from various contexts. The purpose of this letter is to interpret an estimation mechanism of the Bradley-Terry model from the viewpoint of flatness, a fundamental notion used in information geometry. Based on this point of view, a new estimation method is proposed on a framework of the em algorithm. The proposed method is different in its objective function from that of conventional methods, especially in treating unobserved comparisons, and it is consistently interpreted in a probability simplex. An estimation method with weight adaptation is also proposed from a viewpoint of the sensitivity. Experimental results show that the proposed method works appropriately, and weight adaptation improves accuracy of the estimate.