  To build recommender systems that not only consider user-item interactions
represented as ordinal variables, but also exploit the social network
describing the relationships between the users, we develop a hierarchical
Bayesian model termed ordinal graph factor analysis (OGFA), which jointly
models user-item and user-user interactions. OGFA not only achieves good
recommendation performance, but also extracts interpretable latent factors
corresponding to representative user preferences. We further extend OGFA to
ordinal graph gamma belief network, which is a multi-stochastic-layer deep
probabilistic model that captures the user preferences and social communities
at multiple semantic levels. For efficient inference, we develop a parallel
hybrid Gibbs-EM algorithm, which exploits the sparsity of the graphs and is
scalable to large datasets. Our experimental results show that the proposed
models not only outperform recent baselines on recommendation datasets with
explicit or implicit feedback, but also provide interpretable latent
representations.
