Hierarchical Network Models for Exchangeable Structured Interaction Processes. Issue 540 (2nd October 2022)

• Record Type: Journal Article
• Authors: Dempsey, Walter; Oselio, Brandon; Hero, Alfred
• Is Part Of: Journal of the American Statistical Association. Volume 117:Issue 540(2022)
• Page Start: 2056
• Page End: 2073
• Publication Date: 2022-10-02
• Subjects: Exchangeability -- Interaction-labeled networks -- Network models -- Power law -- Sparsity -- Structured interaction data; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2021.1896526
• Languages: English
• ISSNs: 0162-1459

Abstract

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 a statistical model, termed the Pitman-Yor hierarchical vertex components model (PY-HVCM), that is well suited for structured interaction data. The proposed PY-HVCM effectively models complex relational data by partial pooling of local information via a latent, shared population-level distribution. The PY-HCVM is a canonical example of hierarchical vertex components models —a subfamily of models for exchangeable structured interaction-labeled networks, that is, networks invariant to interaction relabeling. Theoretical analysis and supporting simulations provide clear model interpretation, and establish global sparsity and power law degree distribution. A computationally tractable Gibbs sampling algorithm is derived for inferring sparsity and power law properties of complex networks. 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.