Posterior Contraction Rates for Stochastic Block Models

Prasenjit Ghosh (), Debdeep Pati () and Anirban Bhattacharya ()
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Prasenjit Ghosh: Texas A&M University
Debdeep Pati: Texas A&M University
Anirban Bhattacharya: Texas A&M University

Sankhya A: The Indian Journal of Statistics, 2020, vol. 82, issue 2, No 7, 448-476

Abstract: Abstract With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. The stochastic block model constitutes a classical cluster-exhibiting random graph model for networks. There is a substantial amount of literature devoted to proposing strategies for estimating and inferring parameters of the model, both from classical and Bayesian viewpoints. Unlike the classical counterpart, there is a dearth of theoretical results on the accuracy of estimation in the Bayesian setting. In this article, we undertake a theoretical investigation of the posterior distribution of the parameters in a stochastic block model. In particular, we show that one obtains near-optimal rates of posterior contraction with routinely used multinomial-Dirichlet priors on cluster indicators and uniform or general Beta priors on the probabilities of the random edge indicators. Our theoretical results are corroborated through a small scale simulation study.

Keywords: Bayesian asymptotics; Stochastic block models; Clustering; Multinomial-Dirichlet; Networks; Posterior contraction; Random graphs; Primary 62G07; 62G20; secondary 60K35 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13171-019-00180-5

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