Department of Integrated Information Technology, Aoyama Gakuin University, Chuo, Sagamihara, Kanagawa 252-5258, Japan.
Neural Comput. 2011 Jun;23(6):1623-59. doi: 10.1162/NECO_a_00129. Epub 2011 Mar 11.
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.
布拉德利-特里模型是一种通过使用项目的成对比较结果来表示个人偏好或排名数据的统计模型。为了对模型进行估计，已经从各种角度提出了几种基于加权 Kullback-Leibler 散度和的方法。本文的目的是从信息几何中使用的基本概念“平坦度”的角度解释布拉德利-特里模型的估计机制。基于这一观点，在 EM 算法的框架上提出了一种新的估计方法。与传统方法相比，该方法在目标函数上有所不同，特别是在处理未观察到的比较方面，并且在概率单纯形中进行了一致的解释。还从敏感性的角度提出了一种带权适应的估计方法。实验结果表明，所提出的方法是有效的，并且权重自适应提高了估计的准确性。
