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Motivated by the connections between collaborative filtering and networkclustering, we consider a network-based approach to improving rating predictionin recommender systems. We propose a novel Bipartite Mixed-MembershipStochastic Block Model ($\mathrm{BM}^2$) with a conjugate prior from theexponential family. We derive the analytical expression of the model andintroduce a variational Bayesian expectation-maximization algorithm, which iscomputationally feasible for approximating the untractable posteriordistribution. We carry out extensive simulations to show that $\mathrm{BM}^2$provides more accurate inference than standard SBM with the emergence ofoutliers. Finally, we apply the proposed model to a MovieLens dataset and findthat it outperforms other competing methods for collaborative filtering.

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