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.
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