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 of 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 can avoid dimension reduction, estimate latent variables and model parameters more accurately, and facilitate posterior inference. In this article, we develop a novel, computationally feasible Bayesian ICA method with population-derived priors on both the spatial ICs and their temporal correlation (that is, their FC). For the latter, we consider two priors: the inverse-Wishart, which is conjugate but is not ideally suited for modeling correlation matrices; and a novel informative prior for correlation matrices. For each prior, we derive a variational Bayes algorithm to estimate the model variables and facilitate posterior inference. Through extensive simulation studies, we evaluate the performance of the proposed methods and benchmark against existing approaches. We also analyze fMRI data from over 400 healthy adults in the Human Connectome Project. We find that our Bayesian ICA model and algorithms result in more accurate measures of functional connectivity and spatial brain features. Our novel prior for correlation matrices is more computationally intensive than the inverse-Wishart but provides improved accuracy and inference. The proposed framework is applicable to single-subject analysis, making it potentially clinically viable.