Nondiagonal Mixture of Dirichlet Network Distributions for Analyzing a Stock Ownership Network

TL;DR

This paper introduces a Bayesian nonparametric edge exchangeable block model that better captures properties of complex networks like sparsity and heavy-tailed degrees, improving link prediction over traditional SBMs.

Contribution

The paper proposes a novel edge exchangeable block model that incorporates key features of complex networks and infers latent structures more effectively than existing SBMs.

Findings

Outperforms state-of-the-art SBMs in link prediction

Successfully models sparsity and heavy-tailed degree distributions

Demonstrated on synthetic and real-world stock ownership data

Abstract

Block modeling is widely used in studies on complex networks. The cornerstone model is the stochastic block model (SBM), widely used over the past decades. However, the SBM is limited in analyzing complex networks as the model is, in essence, a random graph model that cannot reproduce the basic properties of many complex networks, such as sparsity and heavy-tailed degree distribution. In this paper, we provide an edge exchangeable block model that incorporates such basic features and simultaneously infers the latent block structure of a given complex network. Our model is a Bayesian nonparametric model that flexibly estimates the number of blocks and takes into account the possibility of unseen nodes. Using one synthetic dataset and one real-world stock ownership dataset, we show that our model outperforms state-of-the-art SBMs for held-out link prediction tasks.