标题： 贝叶斯社区检测 显示英文标题

标题： Bayesian Community Detection

摘要： 我们引入了随机块模型中已知类别数量的情况下潜在类别结构的贝叶斯估计量。该估计量对应于类别比例上的狄利克雷先验、类别标签上的广义伯努利先验以及边概率上的Beta先验的后验众数。 我们证明了当网络中节点的期望度至少为阶 $\log^2{n}$ 时，该估计量是强一致的，其中 $n$ 是网络中的节点数。 显示英文摘要

摘要： We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a generalized Bernoulli prior on the class labels, and a beta prior on the edge probabilities. We show that this estimator is strongly consistent when the expected degree is at least of order $\log^2{n}$, where $n$ is the number of nodes in the network.