Improved and Scalable Bradley-Terry Model for Collaborative Ranking

In collaborative ranking, the Bradley-Terry (BT) model is widely used for modeling pairwise user preferences. However, when this model is combined with matrix factorization on sparsely observed ratings, a challenging identifiability issue arises since the optimization will involve non-convex constraints. Besides, in some situations, fitting the Bradley-Terry model yields a numerical challenge as it may include an objective function that is unbounded from below. In this paper, we will discuss and develop a simple strategy to resolve these issues. Specifically, we propose an Improved-BT model by adding a penalty term, and we develop two parallel algorithms to make Improved-BT model scalable. Through extensive experiments on benchmark datasets, we show that our proposed method outperforms many considered state-of-the-art collaborative ranking approaches in terms of both ranking performance and time efficiency.