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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02061401
Contributor : Catherine Matias <>
Submitted on : Friday, March 8, 2019 - 9:55:00 AM
Last modification on : Monday, December 14, 2020 - 5:40:21 PM
Long-term archiving on: : Monday, June 10, 2019 - 3:56:56 PM

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  • HAL Id : hal-02061401, version 1
  • ARXIV : 1903.04306

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Léa Longepierre, Catherine Matias. Consistency of the maximum likelihood and variational estimators in a dynamic stochastic block model. 2019. ⟨hal-02061401v1⟩

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