Hierarchical network models for structured exchangeable interaction processes

TL;DR

This paper introduces hierarchical edge exchangeable models for structured interaction networks, capturing complex data like emails and scientific collaborations, with theoretical properties, efficient algorithms, and real-world applications.

Contribution

It proposes the hierarchical vertex components model, a novel approach that pools information through shared distributions and demonstrates theoretical properties and practical effectiveness.

Findings

Model exhibits global sparsity and power-law degree distribution.

Supports structured interaction data like emails and academic collaborations.

Provides a Gibbs sampling algorithm for inference.

Abstract

Network data often arises via a series of structured interactions among a population of constituent elements. E-mail exchanges, for example, have a single sender followed by potentially multiple receivers. Scientific articles, on the other hand, may have multiple subject areas and multiple authors. We introduce hierarchical edge exchangeable models for the study of these structured interaction networks. In particular, we introduce the hierarchical vertex components model as a canonical example, which partially pools information via a latent, shared population-level distribution. Theoretical analysis and supporting simulations provide clear model interpretation, and establish global sparsity and power-law degree distribution. A computationally tractable Gibbs algorithm is derived. We demonstrate the model on both the Enron e-mail dataset and an ArXiv dataset, showing goodness of fit of the model via posterior predictive validation.