Partition–Mallows Model and Its Inference for Rank Aggregation

Abstract

Learning how to aggregate ranking lists has been an active research area for many years and its advances have played a vital role in many applications ranging from bioinformatics to internet commerce. The problem of discerning reliability of rankers based only on the rank data is of great interest to many practitioners, but has received less attention from researchers. By dividing the ranked entities into two disjoint groups, that is, relevant and irrelevant/background ones, and incorporating the Mallows model for the relative ranking of relevant entities, we propose a framework for rank aggregation that can not only distinguish quality differences among the rankers but also provide the detailed ranking information for relevant entities. Theoretical properties of the proposed approach are established, and its advantages over existing approaches are demonstrated via simulation studies and real-data applications. Extensions of the proposed method to handle partial ranking lists and conduct covariate-assisted rank aggregation are also discussed.

KEYWORDS:

• Covariate-assisted aggregation
• Heterogeneous rankers
• Mallows model
• Meta-analysis
• Partial ranking lists

Supplementary Materials

The Supplementary Materials include the numerical supports of our assumptions for the model setting, more detailed simulation results and proofs of the Theorems.

Additional information

Funding

This research is supported in part by the National Natural Science Foundation of China (grant nos. 11771242 and 11931001), Beijing Academy of Artificial Intelligence (grant BAAI2019ZD0103), and the National Science Foundation of USA (grant nos. DMS-1903139 and DMS-1712714). The author Wanchuang Zhu is partially supported by the Australian Research Council (Data Analytics for Resources and Environments, grant no. IC190100031). We thank the two reviewers for their insightful comments and suggestions that helped us improve the article greatly. We also thank Miss Yuchen Wu for helpful discussions at the early stage of this work.