Bayesian brain edge-based connectivity (BBeC): a Bayesian model for brain edge-based connectivity inference

Brain connectivity analysis based on magnetic resonance imaging is crucial for understanding neurological mechanisms. However, edge-based connectivity inference faces significant challenges, particularly the curse of dimensionality when estimating high-dimensional covariance matrices. Existing methods often struggle to account for the unknown latent topological structure among brain edges, leading to inaccurate parameter estimation and unstable inference.

To address these issues, this study proposes a Bayesian hierarchical model based on a finite-dimensional Dirichlet distribution. Unlike non-parametric approaches, our method utilizes a finite-dimensional Dirichlet distribution to model the latent topological structure of brain networks, ensuring constant parameter dimensionality and improving algorithmic stability. We reformulate the covariance matrix structure to guarantee positive definiteness and employ a Metropolis-Hastings algorithm to simultaneously infer network topology and correlation parameters. Furthermore, to alleviate the computational burden of parameter inference in large-scale networks, we optimized the calculation process of the likelihood function to reduce the algorithm's time complexity. Our implementation is available at https://github.com/mimi6501/BBeC.

Simulations validated the recovery of both network topology and correlation parameters across various settings. Furthermore, we quantitatively compared the proposed framework with the Graphical Lasso and a Dirichlet process-based non-parametric Bayesian model. Experimental results show our model offers flexible parameter tuning while outperforming baselines in estimation accuracy and convergence stability. Sensitivity analysis reveals the diagonal adjustment parameter λ has minimal impact on model accuracy, and parameter sampling order has negligible impact on final inference. When applied to the Alzheimer's Disease Neuroimaging Initiative dataset, the model successfully identified structural subnetworks. The identified clusters were not only validated by composite anatomical metrics but also consistent with established findings in the literature, collectively demonstrating the model's reliability. The estimated covariance matrix also revealed that intragroup connection strength is stronger than intergroup connection strength.

This study introduces a Bayesian framework for inferring brain network topology and high-dimensional covariance structures. The model configuration effectively reduces parameter dimensionality while ensuring the positive definiteness of covariance matrices. As a result, it offers an efficient and reliable tool for investigating intrinsic brain connectivity in large-scale neuroimaging studies.