Bayesian nonparametric modeling of heterogeneous populations of networks

The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this context, we propose a novel Bayesian nonparametric model that identifies clusters of networks characterized by similar connectivity patterns. Our approach relies on a location-scale Dirichlet process mixture of centered Erdős–Rényi kernels, with components parametrized by a unique network representative, or mode, and a univariate measure of dispersion around the mode. We demonstrate that this model has full support in the Kullback–Leibler sense and is strongly consistent. An efficient Markov chain Monte Carlo scheme is proposed for posterior inference and clustering of multiple network data. The performance of the model is validated through extensive simulation studies, showing improvements over state-of-the-art methods. Additionally, we present an effective strategy to extend the application of the proposed model to datasets with a large number of nodes. We illustrate our approach with the analysis of human brain network data.

💡 Research Summary

The paper addresses the growing need for statistical methods capable of handling heterogeneous populations of networks, a situation increasingly common in fields such as neuroscience, mobility analysis, and social network studies. The authors propose a novel Bayesian non‑parametric framework that clusters multiple network observations based on similarity of their connectivity patterns. Central to the approach is the use of a location‑scale Dirichlet‑process (DP) mixture of centered Erdős–Rényi (CER) kernels. Each CER kernel is defined by a “mode” graph (C) (the representative network) and a dispersion parameter (\alpha\in(0,1/2)). The kernel’s probability mass function is
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