Modeling and Change Detection for Count-Weighted Multilayer Networks

Abstract

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.

Keywords:

• Network monitoring
• Score test
• Statistical process monitoring
• Variational-EM

Acknowledgements

The authors would like to thank the editor and all anonymous referees for their valuable comments, which have helped us improve this work greatly.

Additional information

Funding

Miss Hang Dong and Dr. Kaibo Wang’s work are supported by the National Natural Science Foundation of China (Key Program) under grant 71731008 and National Key R&D Program of China under grant No. 2017YFF0209400; Dr. Nan Chen’s work is partially supported by Singapore AcRF under grant R-266-000-123-114.