An Extended Mallows Model for Ranked Data Aggregation

• 成果类型: Article
• 署名作者: Li, Han; Xu, Minxuan; Liu, Jun S.; Fan, Xiaodan
• 署名单位: Shenzhen University; Chinese University of Hong Kong; University of California System; University of California Los Angeles; Harvard University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1573733
• 发表日期: 2020
• 页码: 730-746
• 关键词: probability-models; prostate-cancer; integration; inference

摘要

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. for this article are available online.