Partition–Mallows Model and Its Inference for Rank Aggregation

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.