Nonparametric Bayesian models of hierarchical structure in complex networks

TL;DR

This paper introduces two non-parametric Bayesian hierarchical models for complex networks, effectively capturing nested structures and demonstrating competitive predictive performance, with applications in brain connectivity analysis.

Contribution

The paper proposes novel Gibbs fragmentation tree-based Bayesian models for hierarchical network analysis, advancing the ability to detect nested patterns in complex relational data.

Findings

Successfully captured hierarchical structures in simulated networks.

Achieved predictive performance comparable to current state-of-the-art methods.

Demonstrated applicability to real-world brain connectivity data.

Abstract

Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a hierarchically structured model. We propose two non-parametric Bayesian hierarchical network models based on Gibbs fragmentation tree priors, and demonstrate their ability to capture nested patterns in simulated networks. On real networks we demonstrate detection of hierarchical structure and show predictive performance on par with the state of the art. We envision that our methods can be employed in exploratory analysis of large scale complex networks for example to model human brain connectivity.