SetRank: A Setwise Bayesian Approach for Collaborative Ranking from Implicit Feedback

The recent development of online recommender systems has a focus on collaborative ranking from implicit feedback, such as user clicks and purchases. Different from explicit ratings, which reflect graded user preferences, the implicit feedback only generates positive and unobserved labels. While considerable efforts have been made in this direction, the well-known pairwise and listwise approaches have still been limited by various challenges. Specifically, for the pairwise approaches, the assumption of independent pairwise preference is not always held in practice. Also, the listwise approaches cannot efficiently accommodate "ties" due to the precondition of the entire list permutation. To this end, in this paper, we propose a novel setwise Bayesian approach for collaborative ranking, namely SetRank, to inherently accommodate the characteristics of implicit feedback in recommender system. Specifically, SetRank aims at maximizing the posterior probability of novel setwise preference comparisons and can be implemented with matrix factorization and neural networks. Meanwhile, we also present the theoretical analysis of SetRank to show that the bound of excess risk can be proportional to $\sqrt{M/N}$, where $M$ and $N$ are the numbers of items and users, respectively. Finally, extensive experiments on four real-world datasets clearly validate the superiority of SetRank compared with various state-of-the-art baselines.