A semiparametric extension of the stochastic block model for longitudinal networks

• 成果类型: Article
• 署名作者: Matias, C.; Rebafka, T.; Villers, F.
• 署名单位: Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy016
• 发表日期: 2018
• 页码: 665680
• 关键词: maximum-likelihood; Mixture Model; estimators

摘要

We propose an extension of the stochastic block model for recurrent interaction events in continuous time, where every individual belongs to a latent group and conditional interactions between two individuals follow an inhomogeneous Poisson process with intensity driven by the individuals' latent groups. We show that the model is identifiable and estimate it with a semiparametric variational expectation-maximization algorithm. We develop two versions of the method, one using a nonparametric histogram approach with an adaptive choice of the partition size, and the other using kernel intensity estimators. We select the number of latent groups by an integrated classification likelihood criterion. We demonstrate the performance of our procedure on synthetic experiments, analyse two datasets to illustrate the utility of our approach, and comment on competing methods.