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Abstract:
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Although models have been proposed for static networks, such as stochastic block model, exponential network models, under many of the situations, the networks are time-varying. In this talk, we will first introduce a 1-step Markov model, in which edges are placed independently with the same probabilities depending on the former status of the edges. We also construct the consistent estimators of the probabilities. In analyzing the consistency of the estimators, we use Martingale Central Limit Theorem. Simulations are conducted to analyze the properties and behaviors of the estimators. As a generalization, we next introduce a Markov Dynamic Network Model in which the size of the network is growing, and the conditional probabilities are fluctuating according to the size. We also consider estimation of the edge probabilities in this setting, and apply the dynamic models to real-world data.
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