  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.
