Variational Bayesian Inference for Bipartite Mixed-membership Stochastic Block Model with Applications to Collaborative Filtering

Motivated by the connections between collaborative filtering and network clustering, we consider a network-based approach to improving rating prediction in recommender systems. We propose a novel Bipartite Mixed-Membership Stochastic Block Model (${\mathrm{B}\mathrm{M}}^2$) with a conjugate prior from the exponential family. We derive the analytical expression of the model and introduce a variational Bayesian expectation-maximization algorithm, which is computationally feasible for approximating the untractable posterior distribution. We carry out extensive simulations to show that ${\mathrm{B}\mathrm{M}}^2$ provides more accurate inference than standard SBM with the emergence of outliers. Finally, we apply the proposed model to a MovieLens dataset and find that it outperforms other competing methods for collaborative filtering.