BARD
Introduction
Rank aggregation, that is, combining several ranking functions (called base rankers) to get aggregated, usually stronger rankings of a given set of items, is encountered in many disciplines. Most methods in the literature assume that base rankers of interest are equally reliable. It is very common in practice, however, that some rankers are more informative and reliable than others. It is desirable to distinguish high quality base rankers from low quality ones and treat them differently. Some methods achieve this by assigning prespecified weights to base rankers. But there are no systematic and principled strategies for designing a proper weighting scheme for a practical problem. In this article, we propose a Bayesian approach, called Bayesian aggregation of rank data (BARD), to overcome this limitation. By attaching a quality parameter to each base ranker and estimating these parameters along with the aggregation process, BARD measures reliabilities of base rankers in a quantitative way and makes use of this information to improve the aggregated ranking. In addition, we design a method to detect highly correlated rankers and to account for their information redundancy appropriately. Both simulation studies and real data applications show that BARD significantly outperforms existing methods when equality of base rankers varies greatly.
Installation Package
Paper Link
PAMA
Introduction
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.
Installation Package
Reference
- Ke Deng, Simeng Han, Kate J. Li, and Jun S. Liu (2014) Bayesian Aggregation of Order-Based Rank Data. Journal of the American Statistical Association, 109(507), 1023-1039.
- Wanchuang Zhu, Yingkai Jiang, Jun S. Liu and Ke Deng* (2021) Partition-Mallows Model and Its Inference for Rank Aggregation. Online published by Journal of the American Statistical Association.