Modeling and monitoring multilayer attributed weighted directed networks via a generative model

AbstractAs data with network structures are widely seen in diverse applications, the modeling and monitoring of network data have drawn considerable attention in recent years. When individuals in a network have multiple types of interactions, a multilayer network model should be considered to better characterize its behavior. Most existing network models have concentrated on characterizing the topological structure among individuals, and important attributes of individuals are largely disregarded in existing works. In this article, first, we propose a unified static Network Generative Model (static-NGM), which incorporates individual attributes in network topology modeling. The proposed model can be utilized for a general multilayer network with weighted and directed edges. A variational expectation maximization algorithm is developed to estimate model parameters. Second, to characterize the time-dependent property of a network sequence and perform network monitoring, we extend the static-NGM model to a sequential version, namely, the sequential-NGM model, with the Markov assumption. Last, a sequential-NGM chart is developed to detect shifts and identify root causes of shifts in a network sequence. Extensive simulation experiments show that considering attributes improves the parameter estimation accuracy and that the proposed monitoring method also outperforms the three competitive approaches, static-NGM chart, score test-based chart (ST chart) and Bayes factor-based chart (BF chart), in both shift detection and root cause diagnosis. We also perform a case study with Enron E-mail data; the results further validate the proposed method.Keywords: Generative modelmultilayer attributed networkroot cause diagnosisstatistical process control AcknowledgmentsThe authors greatly thank the Department Editor, the Associate Editor and anonymous referees for their helpful comments and suggestions, which have helped us improve this work greatly.Data availability statementThe data that support the findings of this study are openly available at http://www.cs.cmu.edu/∼enron/Additional informationFundingDr. Wang’s work was supported by the Key Program of the National Natural Science Foundation of China under Grant No. 71932006. Dr. Liang’s work was supported by the National Natural Science Foundation of China under Grant No. 72201212.Notes on contributorsHao WuHao Wu is currently a PhD student at Department of Industrial Engineering, Tsinghua University. He received his BS degree in industrial engineering from Tsinghua University in 2021. His research focuses on network system modeling and monitoring.Qiao LiangQiao Liang is currently an assistant professor in the School of Statistics, Southwestern University of Finance and Economics, Chengdu, China. She received her PhD and BS degrees in industrial engineering from Tsinghua University, Beijing, China. Her research interests are in the areas of statistical modeling and data analytics for manufacturing and service processes, with a focus on statistical process control based on text analytics.Kaibo WangKaibo Wang is a professor in the Department of Industrial Engineering, jointly appointed by the Vanke School of Public Health, Tsinghua University, Beijing, China. He received his BS and MS degrees in mechatronics from Xi’an Jiaotong University, Xi’an, China, and his PhD in industrial engineering and engineering management from the Hong Kong University of Science and Technology, Hong Kong. His research focuses on statistical quality control and data-driven system modelling, monitoring, diagnosis, and control.