An Intransitivity Model for Matchup and Pairwise Comparison

Ranking is a ubiquitous problem setting that appears in many real-world applications. The superior players or objects in the ranking list are oftentimes estimated from matchups and pairwise comparisons. In order to predict the result of unobserved events, various models have been developed to integrate the matchup and pairwise comparison results into a single ranking list of players. Amongst these models, the Bradley-Terry model is the mainstream which achieves the goal by authorizing enriched probabilistic interpretation of players. However, the model suffers from its strong assumption of transitive relationships and becomes vulnerable in practice when intransitive relationships exist. In this paper, we propose a low-rank matrix approach to characterize all players and unify the related works on representation learning of players by rearranging the constructively. Our experimental results on synthetic datasets and real-world datasets show that the proposed model is competitive with the standard models in terms of out-of-sample predictive performance and consistency of model interpretation.