Edge Exchangeable Models for Interaction Networks. Issue 523 (3rd July 2018)

• Record Type: Journal Article
• Authors: Crane, Harry; Dempsey, Walter
• Is Part Of: Journal of the American Statistical Association. Volume 113:Issue 523(2018)
• Page Start: 1311
• Page End: 1326
• Publication Date: 2018-07-03
• Subjects: Edge exchangeability -- Edge-labeled network -- Exchangeable random graph -- Interaction data -- Power-law distribution -- Scale-free network -- Sparse network; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2017.1341413
• Languages: English
• ISSNs: 0162-1459

Abstract

ABSTRACT: Many modern network datasets arise from processes of interactions in a population, such as phone calls, email exchanges, co-authorships, and professional collaborations. In such interaction networks, the edges comprise the fundamental statistical units, making a framework for edge-labeled networks more appropriate for statistical analysis. In this context, we initiate the study of edge exchangeable network models and explore its basic statistical properties. Several theoretical and practical features make edge exchangeable models better suited to many applications in network analysis than more common vertex-centric approaches. In particular, edge exchangeable models allow for sparse structure and power law degree distributions, both of which are widely observed empirical properties that cannot be handled naturally by more conventional approaches. Our discussion culminates in the Hollywood model, which we identify here as the canonical family of edge exchangeable distributions. The Hollywood model is computationally tractable, admits a clear interpretation, exhibits good theoretical properties, and performs reasonably well in estimation and prediction as we demonstrate on real network datasets. As a generalization of the Hollywood model, we further identify the vertex components model as a nonparametric subclass of models with a convenient stick breaking construction.