Inference and Generating Method for Extremely Sparse Networks

Valentin Kilian, Benjamin Guedj, Francois Caron

Keywords: Bayesian nonparametrics, Mixture, Point process, Random graphs, Graphex, Graph Generative Models, Structured Inference

TL;DR: We resolve the tension between exchangeability and extreme sparsity in network modelling. We also provide the method for fitting our model to observations.

Abstract: Generative models for real-world networks face a fundamental challenge in reconciling the desirable property of exchangeability with the empirical observation of sparsity. The Caron-Fox framework, which leverages Kallenberg exchangeability and Completely Random Measures (CRMs), provides a principled approach to this problem. However, existing models within this class typically generate graphs where the number of edges scales super-linearly with the number of nodes ($E \propto N^{1+\epsilon}$). In this work, we present a novel CRM with rapid variation that, when integrated into the Caron-Fox model, generates graph sequences in an extremely sparse regime. We also derive a posterior inference method to fit our model to an observed graph. This workshop paper summarizes the key results of our recent publication, introducing the model, outlining its theoretical underpinnings, and presenting the inference procedure.

Submission Number: 15