Consistent Estimation of Dynamic and Multi-Layer Networks

• Activity Number: 378
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 11:35 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Qiuyi Han* and Edo Airoldi and Kevin Xu
• Companies: Harvard University and Harvard University and Technicolor
• Keywords: dynamic network ; consistency ; stochastic block model

Abstract

Dynamic networks where edges appear and disappear over time and multi-layer networks that deal with multiple types of connections arise in many applications. Though there are models tailored to specific application, no asymptotic analysis has been done beyond single network models. We propose the multi-graph stochastic block model, which serves as a foundation for both dynamic and multi-layer networks. We provide sufficient conditions for consistency of the spectral clustering and maximum-likelihood estimates, which is first-of-its-kind to the authors' knowledge. Moreover we extend inference techniques in the analysis of single networks, namely maximum-likelihood estimation, spectral clustering, and variational approximation, to the multi-graph stochastic block model. We verify the conditions for our results via simulation and demonstrate that the conditions are practical. In addition, we develop hierarchical model based on the multi-graph stochastic block model and apply the model to two real data sets: a dynamic social network and a multi-layer social network, resulting in block estimates that reveal network structure in both cases.