论文标题
随机块模型和图形的经验贝叶斯方法：收缩估计和模型选择
An empirical Bayes Approach to stochastic blockmodels and graphons: shrinkage estimation and model selection
论文作者
论文摘要
Graphon（W-Graph），包括随机块模型作为一种特殊情况，已广泛用于建模和分析网络数据。该随机图模型通过其图形函数进行了充分的特征，并且对图形函数的估计获得了许多最近的研究兴趣。大多数现有的作品都集中在模型潜在空间中的社区检测，同时采用简单的最大可能性或贝叶斯的估算值，或者给定标识的社区的贝叶斯估计值或连接参数。在这项工作中，我们提出了一个层次二项式模型，并开发了一种新型的经验贝叶斯估计随机块模型的连通性矩阵，以近似Graphon函数。基于我们的层次模型的可能性，我们进一步介绍了选择社区数量的模型选择标准。广泛的模拟和两个井井有条的社交网络的数值结果证明了我们在估计准确性和模型选择方面的优越性。
The graphon (W-graph), including the stochastic block model as a special case, has been widely used in modeling and analyzing network data. This random graph model is well-characterized by its graphon function, and estimation of the graphon function has gained a lot of recent research interests. Most existing works focus on community detection in the latent space of the model, while adopting simple maximum likelihood or Bayesian estimates for the graphon or connectivity parameters given the identified communities. In this work, we propose a hierarchical Binomial model and develop a novel empirical Bayes estimate of the connectivity matrix of a stochastic block model to approximate the graphon function. Based on the likelihood of our hierarchical model, we further introduce a model selection criterion for choosing the number of communities. Numerical results on extensive simulations and two well-annotated social networks demonstrate the superiority of our approach in terms of estimation accuracy and model selection.
