# Hierarchical network models for structured exchangeable interaction processes

arXiv: https://arxiv.org/abs/1901.09982 · HTML: https://mlsanity.com/paper/1901.09982/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2019.

## Built on by (most cited first, 1 of 1)

- [Nonparametric Modeling of Higher-Order Interactions via Hypergraphons](https://mlsanity.com/paper/2105.08678/) (2021)

## Abstract (arXiv)

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.