BSNMani: Bayesian scalar-on-network regression with manifold learning

Brain connectivity analysis is crucial for understanding brain structure and neurological function, shedding light on the mechanisms of mental illness. To study the association between individual brain connectivity networks and the clinical characteristics, we develop BSNMani: a Bayesian scalar-on-network regression model with manifold learning. BSNMani comprises two components: the network manifold learning model for brain connectivity networks, which extracts shared connectivity structures and subject-specific network features, and the joint predictive model for clinical outcomes, which studies the association between clinical phenotypes and subject-specific network features while adjusting for potential confounding covariates. For posterior computation, we develop a novel two-stage hybrid algorithm combining Metropolis-Adjusted Langevin Algorithm (MALA) and Gibbs sampling. Our method is not only able to extract meaningful subnetwork features that reveal shared connectivity patterns but can also reveal their association with clinical phenotypes, further enabling clinical outcome prediction. We demonstrate our method through simulations and through its application to real resting-state fMRI data from a study focusing on Major Depressive Disorder (MDD). Our approach sheds light on the intricate interplay between brain connectivity and clinical features, offering insights that can contribute to our understanding of psychiatric and neurological disorders as well as mental health.