The existence of maximum likelihood estimates in the Bradley-Terry model and its extensions

A Bayesian nonparametric approach for generalized Bradley-Terry models in random environment

This paper deals with the estimation of the unknown distribution of hidden random variables from the observation of pairwise comparisons between these variables. This problem is inspired by recent developments on Bradley-Terry models in random environment since this framework happens to be relevant to predict for instance the issue of a championship from the observation of a few contests per team. This paper provides three contributions on a Bayesian nonparametric approach to solve this problem. First, we establish contraction rates of the posterior distribution. We also propose a Markov Chain…

Grouped sparse paired comparisons in the Bradley-Terry model

In a wide class of paired comparisons, especially in the sports games, in which all subjects are divided into several groups, the intragroup comparisons are dense and the intergroup comparisons are sparse. Typical examples include the NFL regular season. Motivated by these situations, we propose group sparsity for paired comparisons and show the consistency and asymptotical normality of the maximum likelihood estimate in the Bradley-Terry model when the number of parameters goes to infinity in this paper. Simulations are carried out to illustrate the group sparsity and asymptotical results.

基于成对比较的广义Bradley-Terry评分估计模型

Generalized Bradley-Terry Models for Score Estimation from Paired Comparisons

本文提出广义Bradley-Terry（GBT）模型族，统一处理离散或连续成对比较，并证明其负对数似然严格凸、MAP估计存在唯一且对比较单调和Lipschitz弹性，兼具理论保证与实用价值。

Uncertainty quantification in the Bradley-Terry-Luce model

The Bradley-Terry-Luce (BTL) model is a benchmark model for pairwise comparisons between individuals. Despite recent progress on the first-order asymptotics of several popular procedures, the understanding of uncertainty quantification in the BTL model remains largely incomplete, especially when the underlying comparison graph is sparse. In this paper, we fill this gap by focusing on two estimators that have received much recent attention: the maximum likelihood estimator (MLE) and the spectral estimator. Using a unified proof strategy, we derive sharp and uniform non-asymptotic expansions for…

一般比较图下的Bradley-Terry模型

Bradley-Terry model under general comparison graphs

本文在一般比较图下建立了Bradley-Terry模型MLE的一致性和渐近正态性，误差界由有效电阻和谱间隙刻画，适用于随机图设计。

通过梯度下降和Bradley-Terry模型实现个体公平性

Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models

提出一种从三元组查询中学习马氏距离度量的算法，结合谱初始化与梯度下降，在非凸损失下快速收敛到真实度量，并证明估计度量下的个体公平性足以近似真实度量下的公平性。

最小最大假设检验用于布雷德利-蒂尔-刘模型

Minimax Hypothesis Testing for the Bradley-Terry-Luce Model

本文提出了一种基于最小最大理论的假设检验方法，用于判断给定的成对比较数据是否源自布雷德利-蒂尔-刘模型，并通过实验验证了该方法的性能。

维数增加的随机图模型中的似然比检验

Likelihood ratio tests in random graph models with increasing dimensions

本文研究了$β$-模型和Bradley-Terry模型中维数增加时的Wilks现象，针对特定原假设和齐性原假设推导了似然比统计量的渐近分布，并开发了适用于更广随机图模型的渐近展开方法。

基于比较的偏好学习模型中在保持单调性的同时实现泛化

Generalizing while preserving monotonicity in comparison-based preference learning models

针对现有基于比较的偏好学习模型难兼顾单调性与泛化性的问题，提出带扩散先验的线性广义布拉德利-特里模型，给出保证单调性的嵌入充分条件，实验验证其准确率更优，有限数据集下效果突出。

成对比较模型中参数估计存在性与唯一性条件的比较分析

Comparative analysis of the existence and uniqueness conditions of parameter estimation in paired comparison models

本文研究三选择成对比较模型极大似然估计的存在唯一性，推广并比较已有充分条件，模拟表明新条件更能有效识别最大值存在。

一个精确无偏的半参数最大拟似然框架，其在存在并列时是完整的

An exact unbiased semi-parametric maximum quasi-likelihood framework which is complete in the presence of ties

本文提出了一种新的半参数最大拟似然框架，用于处理存在并列的排名数据，通过扩展Kemeny度量和相关协方差形式，实现对总体相关性的直接推断，并与Bradley-Terry和Thurstone模型建立等价性。