An Extended Mallows Model for Ranked Data Aggregation
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AbstractIn 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.
Acceptance Date05/01/2019
All Author(s) ListHan Li, Minxuan Xu, Jun S. Liu, Xiaodan Fan
Journal nameJournal of the American Statistical Association
Volume Number115
Issue Number530
PublisherTaylor & Francis
Pages730 - 746
LanguagesEnglish-United States
KeywordsConsensus ranking, Kendall tau distance, Rank aggregation, Rank coefficient

Last updated on 2021-15-10 at 23:37