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A state-space mixed membership blockmodel for dynamic network tomography
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.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS311 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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