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June 2010 A state-space mixed membership blockmodel for dynamic network tomography
Eric P. Xing, Wenjie Fu, Le Song
Ann. Appl. Stat. 4(2): 535-566 (June 2010). DOI: 10.1214/09-AOAS311

Abstract

In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. In this paper we propose a model-based approach to analyze what we will refer to as the dynamic tomography of such time-evolving networks. Our approach offers an intuitive but powerful tool to infer the semantic underpinnings of each actor, such as its social roles or biological functions, underlying the observed network topologies. Our model builds on earlier work on a mixed membership stochastic blockmodel for static networks, and the state-space model for tracking object trajectory. It overcomes a major limitation of many current network inference techniques, which assume that each actor plays a unique and invariant role that accounts for all its interactions with other actors; instead, our method models the role of each actor as a time-evolving mixed membership vector that allows actors to behave differently over time and carry out different roles/functions when interacting with different peers, which is closer to reality. We present an efficient algorithm for approximate inference and learning using our model; and we applied our model to analyze a social network between monks (i.e., the Sampson’s network), a dynamic email communication network between the Enron employees, and a rewiring gene interaction network of fruit fly collected during its full life cycle. In all cases, our model reveals interesting patterns of the dynamic roles of the actors.

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Eric P. Xing. Wenjie Fu. Le Song. "A state-space mixed membership blockmodel for dynamic network tomography." Ann. Appl. Stat. 4 (2) 535 - 566, June 2010. https://doi.org/10.1214/09-AOAS311

Information

Published: June 2010
First available in Project Euclid: 3 August 2010

zbMATH: 1194.62133
MathSciNet: MR2758639
Digital Object Identifier: 10.1214/09-AOAS311

Keywords: Bayesian inference , Dynamic networks , gene regulation network , Graphical model , mixed membership model , mixed membership stochastic blockmodels , Network tomography , Social network , state-space models , Time-varying networks , variational inference

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.4 • No. 2 • June 2010
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