Electronic Journal of Statistics

Consistency of the maximum likelihood and variational estimators in a dynamic stochastic block model

Léa Longepierre and Catherine Matias

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We consider a dynamic version of the stochastic block model, in which the nodes are partitioned into latent classes and the connection between two nodes is drawn from a Bernoulli distribution depending on the classes of these two nodes. The temporal evolution is modeled through a hidden Markov chain on the nodes memberships. We prove the consistency (as the number of nodes and time steps increase) of the maximum likelihood and variational estimators of the model parameters, and obtain upper bounds on the rates of convergence of these estimators. We also explore the particular case where the number of time steps is fixed and connectivity parameters are allowed to vary.

Article information

Electron. J. Statist., Volume 13, Number 2 (2019), 4157-4223.

Received: April 2019
First available in Project Euclid: 22 October 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F12: Asymptotic properties of estimators

Maximum likelihood estimation dynamic network dynamic stochastic block model variational estimation temporal network

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Longepierre, Léa; Matias, Catherine. Consistency of the maximum likelihood and variational estimators in a dynamic stochastic block model. Electron. J. Statist. 13 (2019), no. 2, 4157--4223. doi:10.1214/19-EJS1624. https://projecteuclid.org/euclid.ejs/1571709693

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