Consistency and Asymptotic Normality of Stochastic Block Models Estimators from Sampled Data

Abstract

Statistical analysis of network is an active research area and the literature counts a lot of papers concerned with network models and statistical analysis of networks. However, very few papers deal with missing data in network analysis and we reckon that, in practice, networks are often observed with missing values. In this paper we focus on the Stochastic Block Model with valued edges and consider a MCAR setting by assuming that every dyad (pair of nodes) is sampled identically and independently of the others with probability $\rho >0$. We prove that maximum likelihood estimators and its variational approximations are consistent and asymptotically normal in the presence of missing data as soon as the sampling probability $\rho$ satisfies $\rho \gg \log (n)/n$.

arXiv comment32 pages, 0 figures. arXiv admin note: text overlap with arXiv:1704.06629

References in corpus (5)

• Cooperative Game Theory Approaches for Network Partitioning
• Modeling social networks from sampled data
• Stochastic blockmodels with growing number of classes
• Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels
• Uncovering latent structure in valued graphs: A variational approach

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