Partition-Mallows Model and Its Inference for Rank Aggregation

TL;DR

This paper introduces the Partition-Mallows model for rank aggregation, which distinguishes relevant from irrelevant entities, assesses ranker reliability, and provides detailed rankings, supported by theoretical analysis and empirical validation.

Contribution

It proposes a novel Partition-Mallows framework that separates relevant and irrelevant entities and models their rankings, advancing rank aggregation methods.

Findings

The model effectively distinguishes ranker quality differences.

It accurately ranks relevant entities in simulations and real data.

Extensions handle partial rankings and covariate information.

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, i.e., 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.