bayesian-adaptive-latent-mixture-brain-connectome

name	bayesian-adaptive-latent-mixture-brain-connectome
description	Bayesian adaptive latent mixture model for zero-inflated weighted brain connectome analysis. Use when analyzing structural/functional brain networks with many zero-valued edges, modeling subject-level mixture of shared connectivity templates, or performing Bayesian inference on connectome data with Hurdle likelihoods.
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2605.12901","published":"2026-05-13","authors":"Hsin-Hsiung Huang, Yuh-Haur Chen, Teng Zhang","tags":["bayesian","brain-connectome","zero-inflated","latent-mixture","HCP","hamiltonian-monte-carlo"]}

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

arXiv:2605.12901 | Submitted 13 May 2026 | stat.ME, stat.AP, stat.CO

Core Concept

Replicated weighted brain networks exhibit many structural zeros (absent edges) alongside heterogeneous non-zero edge strengths. In structural connectomics, this zero-inflation coincides with subjects expressing overlapping (rather than discrete) connectivity patterns. This paper proposes a Bayesian adaptive latent mixture model that 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.

Key Insights

1. Zero-Inflated Weighted Networks: Uses a Hurdle likelihood model that separates the binary event of edge existence from the conditional distribution of edge strength given existence. A sparsity-coupling parameter θ enables absent edges to be either independent of, or informative about, latent connectivity.

2. Shared Low-Rank Templates: Each subject's connectome is a convex combination (simplex mixture) of shared low-rank latent score matrices (templates), capturing overlapping rather than discrete connectivity patterns.

3. Theoretical Guarantees: Establishes posterior consistency, local asymptotic normality, a Bernstein-von Mises approximation, and predictive consistency for an identifiable quotient-space estimand under fixed-template scenarios.

4. Computation via Transformed HMC: Uses transformed Hamiltonian Monte Carlo on unconstrained coordinates. Selects number of templates via predictive fit, held-out link prediction, and template stability.

5. Human Connectome Project Validation: Applied to HCP data, the model recovers stable latent score patterns and heterogeneous subject-level mixtures. Behavioral analyses serve as exploratory annotations.

Method Components

Hurdle Likelihood

P(Y_ij | θ, π_ij, μ_ij) = 
  (1-π_ij)^(1-Y_ij) × [π_ij × f(Y_ij | μ_ij)]^(Y_ij)

Where Y_ij is edge weight, π_ij is edge existence probability, and μ_ij is conditional edge strength.

Latent Mixture Model

Each subject network A^(s) is modeled as:

A^(s) = Σ_{k=1}^K w_k^(s) × L_k + ε

Where w^(s) is a simplex weight vector over K templates, L_k are shared low-rank latent score matrices.

Applications

• Structural connectome analysis with tractography-derived edge weights (often zero-inflated)
• Functional connectome analysis where correlation thresholds induce zeros
• Cross-subject connectome comparison with heterogeneous connectivity patterns
• Connectome-based behavioral prediction with uncertainty quantification
• Template discovery in population-level brain network studies

Activation Keywords

• zero-inflated brain connectome
• Bayesian latent mixture model
• Hurdle likelihood connectome
• structural connectome HCP
• Hamiltonian Monte Carlo connectome
• Bayesian adaptive mixture
• shared latent template brain network
• posterior consistency connectome
• overlapping connectivity patterns

References

• Huang, Chen & Zhang (2026). A Bayesian Adaptive Latent Mixture Model for Zero-Inflated Weighted Brain Connectome Analysis. arXiv:2605.12901