There are various parametric models for analyzing pairwise comparison data, including the Bradley-Terry-Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this work, we study a flexible model for pairwise comparisons, under which the probabilities of outcomes are required only to satisfy a natural form of stochastic transitivity. This class includes several parametric models including the BTL and Thurstone models as special cases, but is considerably more general. We provide various examples of models in this broader stochastically transitive class for which classical parametric models provide poor fits. Despite this greater flexibility, we show that the matrix of probabilities can be estimated at the same rate as in standard parametric models. On the other hand, unlike in the BTL and Thurstone models, computing the least-squares estimate in the stochastically transitive model is non-trivial, and we explore various computationally tractable alternatives. We show that a simple singular value thresholding algorithm is statistically consistent but does not achieve the minimax rate. We then propose and study algorithms that achieve the minimax rate over interesting sub-classes of the full stochastically transitive class. We complement our theoretical results with thorough numerical simulations.

本文研究了一种可灵活处理成对比较数据的模型，该模型只需要满足自然形式的随机可比性即可，相较于传统的参数模型更加通用，提供了各种重要的子类来提高计算可行性，该模型的矩阵概率也可以像标准参数模型那样进行估计。

成对比较的随机传递模型：统计与计算问题