Edge exchangeable models for network data

TL;DR

This paper introduces edge exchangeability as a new framework for modeling network data, enabling the representation of sparse and power law degree distributions that traditional vertex exchangeable models cannot capture.

Contribution

It proposes the concept of edge exchangeability, providing a new class of nonparametric models for network data that better reflect empirical network behaviors.

Findings

Edge exchangeable models can represent sparse networks.

The paper characterizes a tractable family of edge exchangeable distributions.

Demonstrates the usefulness of these models in estimation, prediction, and testing.

Abstract

Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question of how network data can be modeled in a way that reflects known empirical behaviors and respects basic statistical principles. We address this question by observing that edges, not vertices, act as the statistical units in networks constructed from interaction data, making a theory of edge-labeled networks more natural for many applications. In this context we introduce the concept of {\em edge exchangeability}, which unlike its vertex exchangeable counterpart admits models for networks with sparse and/or power law structure. Our characterization of edge exchangeable networks gives rise to a class of nonparametric models, akin to graphon models in the vertex exchangeable setting. Within this class, we identify a tractable family of distributions with a clear interpretation and suitable theoretical properties, whose significance in estimation, prediction, and testing we demonstrate.