December 2022 Extended stochastic block models with application to criminal networks
Sirio Legramanti, Tommaso Rigon, Daniele Durante, David B. Dunson
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Ann. Appl. Stat. 16(4): 2369-2395 (December 2022). DOI: 10.1214/21-AOAS1595


Reliably learning group structures among nodes in network data is challenging in several applications. We are particularly motivated by studying covert networks that encode relationships among criminals. These data are subject to measurement errors, and exhibit a complex combination of an unknown number of core-periphery, assortative and disassortative structures that may unveil key architectures of the criminal organization. The coexistence of these noisy block patterns limits the reliability of routinely-used community detection algorithms, and requires extensions of model-based solutions to realistically characterize the node partition process, incorporate information from node attributes, and provide improved strategies for estimation and uncertainty quantification. To cover these gaps, we develop a new class of extended stochastic block models (esbm) that infer groups of nodes having common connectivity patterns via Gibbs-type priors on the partition process. This choice encompasses many realistic priors for criminal networks, covering solutions with fixed, random and infinite number of possible groups, and facilitates the inclusion of node attributes in a principled manner. Among the new alternatives in our class, we focus on the Gnedin process as a realistic prior that allows the number of groups to be finite, random and subject to a reinforcement process coherent with criminal networks. A collapsed Gibbs sampler is proposed for the whole esbm class, and refined strategies for estimation, prediction, uncertainty quantification and model selection are outlined. The esbm performance is illustrated in realistic simulations and in an application to an Italian mafia network, where we unveil key complex block structures, mostly hidden from state-of-the-art alternatives.


We are grateful to the Editor, the Associate Editor and the anonymous referees for the valuable comments and the constructive feedbacks, which helped us in improving the preliminary version of this article. We also thank Omiros Papaspiliopoulos for the insightful discussion on model selection techniques.


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Sirio Legramanti. Tommaso Rigon. Daniele Durante. David B. Dunson. "Extended stochastic block models with application to criminal networks." Ann. Appl. Stat. 16 (4) 2369 - 2395, December 2022.


Received: 1 January 2021; Revised: 1 November 2021; Published: December 2022
First available in Project Euclid: 26 September 2022

MathSciNet: MR4489215
zbMATH: 1498.62323
Digital Object Identifier: 10.1214/21-AOAS1595

Keywords: Bayesian nonparametrics , Gibbs-type prior , network , product partition model

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 4 • December 2022
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