Leveraging population information in brain connectivity via Bayesian ICA with a novel informative prior for correlation matrices

Brain functional connectivity (FC), the temporal synchrony between brain networks, is essential to understand the functional organization in the brain and to identify changes due to neurological disorders, development, treatment, and other phenomena. Independent component analysis (ICA) is a matrix decomposition method used extensively for simultaneous estimation of functional brain topography and connectivity. However, estimation of FC via ICA is often sub-optimal due to the use of ad-hoc estimation methods or temporal dimension reduction prior to ICA. Bayesian ICA methods can avoid dimension reduction, produce more accurate estimates of latent variables and model parameters, and facilitate inference via posterior distributions. In this paper, we develop a novel, computationally feasible Bayesian ICA method with population-derived priors on both the spatial ICs and their temporal correlation. For the latter we consider two priors: the inverse-Wishart, which is designed for covariance matrices and has limitations for modeling correlation matrices; and a novel informative prior for correlation matrices. For both choices of prior, we derive a variational Bayes algorithm to estimate the model variables and obtain posterior variances or distributions of quantities of interest. Through extensive realistic simulation studies, we evaluate the performance of the proposed methods and compare them with existing approaches. Finally, we analyze fMRI data from over 400 healthy adults in the Human Connectome Project. We find that our Bayesian ICA algorithms produce highly accurate measures of functional connectivity and spatial brain features. Our informative prior for correlation matrices outperforms the inverse-Wishart, but comes with a higher computational burden. The proposed framework is applicable to single-subject analysis, making it potentially clinically viable.