Nonparametric weighted stochastic block models

TL;DR

This paper introduces a Bayesian nonparametric weighted stochastic block model that infers hierarchical modular structures in weighted networks without prior knowledge of the number of groups, applicable to diverse real-world networks.

Contribution

It develops a flexible, nonparametric Bayesian framework for weighted network analysis that automatically infers the number of communities and their hierarchical organization.

Findings

Successfully applied to global migration networks

Effectively identified community structures in voting and neural data

Demonstrated robustness across different weight types and transformations

Abstract

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the model, which are instead inferred from data. We give a comprehensive treatment of different kinds of edge weights (i.e. continuous or discrete, signed or unsigned, bounded or unbounded), as well as arbitrary weight transformations, and describe an unsupervised model selection approach to choose the best network description. We illustrate the application of our method to a variety of empirical weighted networks, such as global migrations, voting patterns in congress, and neural connections in the human brain.