An Extended Mallows Model for Ranked Data Aggregation

In this article, we study the rank aggregation problem, which aims to find a consensus ranking by aggregating multiple ranking lists. To address the problem probabilistically, we formulate an elaborate ranking model for full and partial rankings by generalizing the Mallows model. Our model assumes that the ranked data are generated through a multistage ranking process that is explicitly governed by parameters that measure the overall quality and stability of the process. The new model is quite flexible and has a closed form expression. Under mild conditions, we can derive a few useful theoretical properties of the model. Furthermore, we propose an efficient statistic called rank coefficient to detect over-correlated rankings and a hierarchical ranking model to fit the data. Through extensive simulation studies and real applications, we evaluate the merits of our models and demonstrate that they outperform the state-of-the-art methods in diverse scenarios. Supplementary materials for this article are available online.本文针对排序聚合问题展开研究，该问题旨在通过整合多个排序列表以生成一致性排序结果。为从概率视角解决该问题，我们通过推广马洛斯模型（Mallows model），针对全排序与部分排序构建了一套精细的排序模型。我们的模型假设，排序数据生成于一个多阶段排序流程，该流程由表征流程整体质量与稳定性的参数显式控制。该新型模型具备较强灵活性，且拥有闭式表达式。在温和条件下，我们可推导出该模型的若干实用理论性质。此外，我们提出了一种名为排序系数的高效统计量，用于检测过度关联的排序结果，同时构建了层级排序模型以适配数据。通过大量仿真实验与实际应用，我们对所提模型的优势进行了评估，并证实其在多种场景下均优于当前主流方法。本文的补充材料可在线获取。