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Abstract:
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Stochastic block models are powerful statistical models to analyze random networks, where nodes are grouped into clusters based on similar connecting probabilities. Recently, time-evolving networks have attracted much attention in fields such as neuroscience, social science, and microbiology. To model time-evolving networks, researchers have generalized stochastic block models to dynamic settings by generalizing the static connecting probabilities to the connecting intensities over time. However, in many applications, the connecting intensities are subject to node-specific time shifts, such as neuron-specific maturation times. Ignoring the unknown time shifts may result in unidentifiability or misclustering in the dynamic stochastic block model. In this paper, we propose a dynamic stochastic block model that incorporates the unknown time shifts. We analyze the identifiability conditions of the model parameters. Using methods for shape invariant models, we propose a semiparametric estimation procedure for simultaneously estimating model parameters including the unknown time shifts. The performance of our method is demonstrated through simulation experiments and a real neural data.
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