Temporal Exponential-Family Random Graph Models with Time-Evolving Latent Block Structure for Dynamic Networks

• Activity Number: 123 - New Challenges and Opportunities in Nonparametric Statistics
• Type: Topic Contributed
• Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kevin Lee* and Amal Agarwal and Lingzhou Xue
• Companies: Western Michigan University and The Pennsylvania State University and Penn State University and National Institute of Statistical Sciences
• Keywords: Dynamic networks; Temporal exponential-family random graph model; Hidden Markov model; Variational inference; Model selection

Abstract

Model-based clustering of dynamic networks has emerged as an essential research topic in statistical network analysis. It is critical to effectively and efficiently model the time-evolving latent block structure of dynamic networks in practice. We present a principled statistical clustering of dynamic networks through the temporal exponential-family random graph models with a hidden Markov structure. The temporal exponential-family random graph models allow us to detect groups based on interesting features of the dynamic networks and the hidden Markov structure is used to infer the time-evolving block structure of dynamic networks. We prove the identification conditions for both network parameters and transition matrix in our proposed model-based clustering. We propose an effective model selection criterion based on the integrated classification likelihood to choosing an appropriate number of clusters. We develop a variational expectation-maximization algorithm to solve the approximate maximum likelihood estimate. The numerical performance of our proposed method is demonstrated in simulation studies and real data applications.