We consider the problem of ranking objects from noisy pairwise comparisons, for example, ranking tennis players from the outcomes of matches. We follow a standard approach to this problem and assume that each object has an unobserved strength and that the outcome of each comparison depends probabilistically on the strengths of the comparands. However, we do not assume to know a priori how skills affect outcomes. Instead, we present an efficient algorithm for simultaneously inferring both the unobserved strengths and the function that maps strengths to probabilities. Despite this problem being under-constrained, we present experimental evidence that the conclusions of our Bayesian approach are robust to different model specifications. We include several case studies to exemplify the method on real-world data sets.

翻译：我们研究从带噪声的成对比较中对对象进行排序的问题，例如根据网球比赛结果对球员进行排名。我们采用解决该问题的标准方法，假设每个对象具有未观测的强度，且每次比较的结果以概率方式依赖于比较对象的强度。然而，我们并不预先假设技能如何影响结果。相反，我们提出一种高效算法，能够同时推断未观测的强度以及将强度映射到概率的函数。尽管该问题存在欠约束性，我们通过实验证据表明，贝叶斯方法的结论对不同模型设定具有鲁棒性。我们包含多个案例研究，以展示该方法在真实数据集上的应用。