Modeling and Change Detection for Count-Weighted Multilayer Networks

In a typical network with a set of individuals, it is common to have multiple types of interactions between two individuals. In practice, these interactions are usually sparse and correlated, which is not sufficiently accounted for in the literature. This article proposes a multilayer weighted stochastic block model (MZIP-SBM) based on a multivariate zero-inflated Poisson (MZIP) distribution to characterize the sparse and correlated multilayer interactions of individuals. A variational-EM algorithm is developed to estimate the parameters in this model. We further propose a monitoring statistic based on the score test of MZIP-SBM model parameters for change detection in multilayer networks. The proposed model and monitoring scheme are validated using extensive simulation studies and the case study from Enron E-mail network.

在由个体集合构成的典型网络中，个体间通常存在多种类型的交互行为。实际场景中，这类交互往往兼具稀疏性与相关性，而现有文献尚未对此进行充分考量。本文提出一种基于多元零膨胀泊松（MZIP）分布的多层加权随机块模型（MZIP-SBM），用于刻画个体间稀疏且相关的多层交互特征。本文设计变分-EM算法以估计该模型的参数。进一步，本文基于MZIP-SBM模型参数的得分检验构建监测统计量，用于实现多层网络的变化检测。通过大规模仿真实验与安然电子邮件网络的案例研究，验证了所提模型与监测方案的有效性。