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Asymptotic comparison of identifying constraints for Bradley-Terry models

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arxiv 2205.04341 v1 pith:7PYJKJAI submitted 2022-05-09 math.ST stat.MEstat.TH

Weichen Wu , Brian W. Junker , Nynke M.D. Niezink This is my paper · ORCID
classification math.STstat.MEstat.TH
keywords bradley-terryasymptoticcomparisonconstraintconstraintsmodelscoresanalysis
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The Bradley-Terry model is widely used for pairwise comparison data analysis. In this paper, we analyze the asymptotic behavior of the maximum likelihood estimator of the Bradley-Terry model in its logistic parameterization, under a general class of linear identifiability constraints. We show that the constraint requiring the Bradley-Terry scores for all compared objects to sum to zero minimizes the sum of the variances of the estimated scores, and recommend using this constraint in practice.

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  1. Energy-Based Preference Model Offers Better Offline Alignment than the Bradley-Terry Preference Model

    cs.LG 2024-12 conditional novelty 6.0 of 10

    EPA, a contrastive preference loss based on an energy-based model with a unique maximum likelihood estimator, outperforms DPO on offline LLM alignment benchmarks.

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