A Bayesian Adaptive Latent Mixture Model for Zero-Inflated Weighted Brain Connectome Analysis

TL;DR

This paper introduces a Bayesian latent mixture model for zero-inflated weighted brain networks, capturing complex connectivity patterns and heterogeneity among subjects with rigorous theoretical guarantees.

Contribution

It proposes a novel Bayesian framework with a hurdle likelihood and adaptive sparsity, advancing analysis of zero-inflated brain connectome data with theoretical validation.

Findings

The model outperforms topology-only baselines in simulations with mixed memberships.

Applied to Human Connectome Project data, it identifies stable latent patterns and subject mixtures.

Theoretical results include posterior consistency and asymptotic normality.

Abstract

Replicated weighted networks often exhibit many structural zeros alongside heterogeneous non-zero edge strengths. In structural connectomics, this zero-inflation coincides with subjects expressing overlapping, rather than discrete, connectivity patterns. To address these features, we propose a Bayesian adaptive latent mixture model for zero-inflated weighted networks. Our approach represents each subject network as a simplex mixture of shared low-rank latent score matrices, integrated with a hurdle likelihood that separates edge existence from conditional edge strength. A sparsity-coupling parameter enables absent edges to be either independent of, or informative about, the latent connectivity. For computation, we employ transformed Hamiltonian Monte Carlo on unconstrained coordinates, selecting the number of templates via predictive fit, held-out link prediction, and template stability. Theoretically, we establish posterior consistency, local asymptotic normality, a Bernstein--von Mises approximation, and predictive consistency for an identifiable quotient-space estimand under a fixed-template scenario. Simulations demonstrate performance gains over topology-only baselines in settings with mixed memberships or structure-informed sparsity. Applied to Human Connectome Project data, the model recovers stable latent score patterns and heterogeneous subject-level mixtures, with behavioural analyses serving strictly as exploratory annotations rather than confirmatory biomarker claims.