Tensor factorization recommender systems with dependency

: Dependency structure in recommender systems has been widely adopted in recent years to improve prediction accuracy. In this paper, we propose an innovative tensor-based recommender system, namely, the Ten- sor Factorization with Dependency (TFD). The proposed method utilizes shared factors to characterize the dependency between different modes, in addition to pairwise additive tensor factorization to integrate information among multiple modes. One advantage of the proposed method is that it provides flexibility for different dependency structures by incorporating shared latent factors. In addition, the proposed method unifies both binary and ordinal ratings in recommender systems. We achieve scalable computation for scarce tensors with high missing rates. In theory, we show the asymptotic consistency of estimators with various loss functions for both binary and ordinal data. Our numerical studies demonstrate that the pro- posed method outperforms the existing methods, especially on prediction accuracy.