随机块模型和图子的经验Bayes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
摘要：
图子（W-图），包括作为特例的随机块模型，已广泛应用于网络数据建模和分析。这种随机图模型的图子函数是一个很好的刻画，图子函数的估计是近年来的一个研究热点。大多数现有的工作集中在潜在空间的模型中的社区检测，而采用简单的极大似然或贝叶斯估计的graphon或连接参数给定的社区。在这项工作中，我们提出了一个分层二项模型，并开发了一个新的经验贝叶斯估计的随机块模型的连接矩阵来近似的图子函数。基于我们的分层模型的可能性，我们进一步引入了一个模型选择标准，用于选择社区的数量。大量的模拟和两个注释良好的社交网络的数值结果表明，我们的方法在估计精度和模型选择方面的优越性。
英文摘要：
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.
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