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 ($\mathrm{BM}^2$) 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 $\mathrm{BM}^2$ 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.

翻译：受协同过滤与网络聚类之间关联的启发，我们考虑一种基于网络的策略来改进推荐系统中的评分预测。我们提出了一种新颖的二部混合隶属度随机块模型（$\mathrm{BM}^2$），并采用来自指数族的共轭先验。我们推导了该模型的解析表达式，并引入了一种变分贝叶斯期望最大化算法，该算法在计算上可行，能够近似难以处理的後验分布。我们通过大量模拟实验表明，当存在异常值时，$\mathrm{BM}^2$比标准SBM提供更准确的推断。最后，我们将所提模型应用于MovieLens数据集，并发现它在协同过滤方面优于其他竞争方法。