Consistent estimation of dynamic and multi-layer block models
Consistent estimation of dynamic and multi-layer block models
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发表时间：
2014-10
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通讯作者：
Qiuyi Han;Kevin S. Xu;E. Airoldi
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作者：
Qiuyi Han;Kevin S. Xu;E. Airoldi
近年来，随机块模型（SBM）估计量的理论分析取得了重大进展。在本文中，我们考虑多图SBM，它作为许多应用程序设置，包括动态和多层网络的基础。我们探索的两个估计的多重图SBM，即谱聚类和最大似然估计（MLE）的渐近性质，作为多层图的层数的增加。我们推导出两个估计的一致性的充分条件，并提出了一个变分近似的MLE，计算上是可行的大型网络。我们通过仿真验证了充分条件，并证明了它们是实用的。此外，我们将该模型应用到两个真实的数据集：一个动态的社会网络和多层社会网络与几种类型的关系。
Significant progress has been made recently on theoretical analysis of estimators for the stochastic block model (SBM). In this paper, we consider the multi-graph SBM, which serves as a foundation for many application settings including dynamic and multi-layer networks. We explore the asymptotic properties of two estimators for the multi-graph SBM, namely spectral clustering and the maximum-likelihood estimate (MLE), as the number of layers of the multi-graph increases. We derive sufficient conditions for consistency of both estimators and propose a variational approximation to the MLE that is computationally feasible for large networks. We verify the sufficient conditions via simulation and demonstrate that they are practical. In addition, we apply the model to two real data sets: a dynamic social network and a multi-layer social network with several types of relations.