Nonparametric Bayes Modeling of Populations of Networks

TL;DR

This paper introduces a Bayesian nonparametric model for analyzing populations of network data, especially in connectomics, offering flexible inference on the entire distribution of network structures with improved performance over existing methods.

Contribution

It develops a novel mixture model leveraging latent space representations for flexible, scalable inference on network populations, with theoretical guarantees and practical advantages.

Findings

Model demonstrates superior fit in simulations.

Application to brain networks shows improved insights.

Efficient Gibbs sampler enables practical inference.

Abstract

Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network-valued data. Available models for a single network are not designed specifically for inference on the entire probability mass function of a network-valued random variable and therefore lack flexibility in characterizing the distribution of relevant topological structures. We propose a flexible Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges is defined via a mixture model which reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations. The formulation leads to an efficient Gibbs sampler and provides simple and coherent strategies for inference and goodness-of-fit assessments. We provide theoretical results on the flexibility of our model and illustrate improved performance --- compared to state-of-the-art models --- in simulations and application to human brain networks.