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June 2020 A random effects stochastic block model for joint community detection in multiple networks with applications to neuroimaging
Subhadeep Paul, Yuguo Chen
Ann. Appl. Stat. 14(2): 993-1029 (June 2020). DOI: 10.1214/20-AOAS1339

Abstract

To analyze data from multisubject experiments in neuroimaging studies, we develop a modeling framework for joint community detection in a group of related networks that can be considered as a sample from a population of networks. The proposed random effects stochastic block model facilitates the study of group differences and subject-specific variations in the community structure. The model proposes a putative mean community structure, which is representative of the group or the population under consideration but is not the community structure of any individual component network. Instead, the community memberships of nodes vary in each component network with a transition matrix, thus modeling the variation in community structure across a group of subjects. To estimate the quantities of interest, we propose two methods: a variational EM algorithm and a model-free “two-step” method called Co-OSNTF which is based on nonnegative matrix factorization. We also develop a resampling-based hypothesis test for differences between community structure in two populations both at the whole network level and node level. The methodology is applied to the COBRE dataset, a publicly available fMRI dataset from multisubject experiments involving schizophrenia patients. Our methods reveal an overall putative community structure representative of the group as well as subject-specific variations within each of the two groups, healthy controls and schizophrenia patients. The model has good predictive ability for predicting community structure in subjects from the same population but outside the training sample. Using our network level hypothesis tests, we are able to ascertain statistically significant difference in community structure between the two groups, while our node level tests help determine the nodes that are driving the difference.

Citation

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Subhadeep Paul. Yuguo Chen. "A random effects stochastic block model for joint community detection in multiple networks with applications to neuroimaging." Ann. Appl. Stat. 14 (2) 993 - 1029, June 2020. https://doi.org/10.1214/20-AOAS1339

Information

Received: 1 April 2019; Revised: 1 March 2020; Published: June 2020
First available in Project Euclid: 29 June 2020

zbMATH: 07239893
MathSciNet: MR4117838
Digital Object Identifier: 10.1214/20-AOAS1339

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.14 • No. 2 • June 2020
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