Electronic Journal of Statistics

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

Léa Longepierre and Catherine Matias

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1571709693

Digital Object Identifier
doi:10.1214/19-EJS1624

Subjects
Primary: 62F12: Asymptotic properties of estimators

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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