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**A state-space mixed membership blockmodel for dynamic network tomography.**
*(English)*
Zbl 1194.62133

Summary: In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. 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 trajectories. 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. 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.

We present an efficient algorithm for approximate inference and learning using our model. 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.

### MSC:

62P25 | Applications of statistics to social sciences |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

65C60 | Computational problems in statistics (MSC2010) |

91D30 | Social networks; opinion dynamics |

### Keywords:

dynamic networks; network tomography; mixed membership stochastic blockmodels; state-space models; time-varying networks; mixed membership model; graphical model; variational inference; Bayesian inference; social network; gene regulation network### Software:

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\textit{E. P. Xing} et al., Ann. Appl. Stat. 4, No. 2, 535--566 (2010; Zbl 1194.62133)

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