用于配对比较数据的保序Bradley-Terry模型
Isotonic Bradley-Terry Model for Paired Comparison Data
- Hitotsubashi University（一桥大学）
- Hitotsubashi Institute for Advanced Study（一桥大学高等研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对配对比较数据的模型设定误差问题，提出交替学习速率参数与逆连接函数的保序Bradley-Terry模型，经实验可提升获胜概率预测与排名性能。
AI中文摘要：
本文研究配对比较数据的预测问题，例如利用匹配选手间的胜负概率数据，预测两名未匹配选手的获胜概率，并根据选手实力顺序对所有选手进行排名。配对比较数据通常采用Bradley-Terry模型和Thurstone-Mosteller模型分析，这些模型通过预定义的逆连接函数变换学习到的速率参数（代表选手实力）的差值来预测获胜概率，并利用学习到的速率参数的顺序进行选手排名。然而，这些模型可能因选择固定的逆连接函数而出现模型设定误差。因此，本研究提出交替使用（次）梯度方法学习速率参数，利用保序回归技术学习逆连接函数。所提模型保证训练误差单调下降，当可用数据不足以建立严格排名时，可能产生精确的平局。我们还通过合成数据及英超联赛（Premier League）、美国职业棒球大联盟（MLB）、ATP网球巡回赛的真实数据进行数值实验，验证了所提模型可提升获胜概率预测和排名性能。
英文摘要：
In this paper, we study prediction problems for paired comparison data, for example, predicting the win probability between two unmatched players and ranking all the players according to the order of their strengths by using win probability data between two matched players. Paired comparison data are typically analyzed using Bradley-Terry and Thurstone-Mosteller models. These models predict the win probability by transforming the difference between learned rate parameters, which represent players'\;strengths, with a pre-specified inverse link function, and employ the order of learned rate parameters for player ranking. However, these models may suffer from model misspecification owing to the selection of a fixed inverse link function. Therefore, in this study, we propose to learn the rate parameters by a (sub-)gradient method and the inverse link function by an isotonic regression technique alternately. The proposed model guarantees monotonic improvement in training error, and is likely to yield an exact tie when the available data is insufficient to establish a strict ranking. We also verified that the proposed model could improve the win probability prediction and ranking performance through numerical experiments with synthetic data and real-world data of football Premier League, baseball MLB, and tennis ATP tour.
