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

2026-05-12

AI Summary

This work addresses the challenges posed by coexisting structural zeros and heterogeneous non-zero edge strengths in weighted brain connectomes, as well as overlapping individual connectivity patterns. To this end, the authors propose a Bayesian adaptive latent mixture model that represents each subject’s network as a mixture over a shared low-rank latent score matrix lying on a simplex. Edge existence and conditional intensity are disentangled via a hurdle likelihood formulation. A sparse coupling parameter flexibly captures the relationship between missing edges and latent structure, and theoretical guarantees—including posterior consistency, local asymptotic normality, and predictive consistency—are established within an identifiable quotient space. Computation leverages transformed Hamiltonian Monte Carlo in unconstrained coordinates, with the number of latent templates selected via predictive fit and leave-one-link-out prediction. Experiments demonstrate superior performance over topological baselines in both synthetic and Human Connectome Project data, reliably recovering latent connectivity motifs and individual-specific heterogeneity.

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.

Problem

• zero-inflated networks
• weighted brain connectome
• heterogeneous connectivity patterns
• structural zeros
• mixed membership

Innovation

• Bayesian adaptive latent mixture model
• zero-inflated weighted networks
• hurdle likelihood
• low-rank latent structure
• sparsity-coupling parameter