An exact algorithm for time-dependent variational inference for the dynamic stochastic block model

摘要

An exact algorithm for estimating the dynamic stochastic block model is proposed. This model assumes a hidden Markov chain for the evolution of the social behavior of a group of individuals at repeated time occasions and may be used to assign these individuals to the latent blocks in a dynamic fashion. For the estimation of this model, the proposed exact algorithm maximizes the target function introduced by Matias and Miele [7]. This function is derived from a variational approximation of the model log-likelihood, based on the assumption that the latent variables identifying the blocks are a posteriori independent across individuals, but not across time occasions. A simulation study is performed to compare the exact algorithm with the approximate maximization algorithm proposed by Matias and Miele [7]. Results show that there is a certain advantage of the first in terms of dynamic assignment of individuals to the latent blocks in comparison to the true blocking structure, as measured by the adjusted Rand index. (C) 2020 Elsevier B.V. All rights reserved.