EXTENDED STOCHASTIC BLOCK MODELS WITH APPLICATION TO CRIMINAL NETWORKS.

Area of Science:

• Network analysis
• Statistical modeling
• Sociology

Background:

• Learning group structures in network data is challenging due to noise and complex patterns.
• Covert networks, like criminal organizations, exhibit unique structures (core-periphery, assortative/disassortative) that are difficult to detect.
• Existing community detection algorithms struggle with noisy, multi-patterned networks.

Purpose of the Study:

• Develop a novel class of extended stochastic block models (esbm) to reliably infer group structures in complex networks.
• Incorporate node attributes and provide robust estimation and uncertainty quantification for network analysis.
• Characterize node partition processes in realistic scenarios, including criminal networks.

Main Methods:

• Introduced extended stochastic block models (esbm) with Gibbs-type priors on the partition process.
• Utilized the Gnedin process as a prior allowing for finite, random, and reinforced group structures.
• Developed a collapsed Gibbs sampler for estimation, prediction, uncertainty quantification, and model selection.

Main Results:

• Demonstrated the effectiveness of esbm in realistic simulations.
• Successfully applied esbm to an Italian mafia network, revealing complex block structures.
• Identified key network architectures previously hidden from state-of-the-art methods.

Conclusions:

• Extended stochastic block models (esbm) offer a powerful and flexible framework for analyzing complex network structures.
• The proposed methods provide reliable group inference, even in the presence of noise and mixed patterns.
• This approach enhances our understanding of organizational structures in covert networks.