Deep Parametric Mixtures for Modeling the Functional Connectome

Functional connectivity between brain regions is often estimated by correlating brain activity measured by resting-state fMRI in those regions. The impact of factors (e.g, disorder or substance use) are then modeled by their effects on these correlation matrices in individuals. A crucial step in better understanding their effects on brain function could lie in estimating connectomes, which encode the correlation matrices across subjects. Connectomes are mostly estimated by creating a single average for a specific cohort, which works well for binary factors (such as sex) but is unsuited for continuous ones, such as alcohol consumption. Alternative approaches based on regression methods usually model each pair of regions separately, which generally produces incoherent connectomes as correlations across multiple regions contradict each other. In this work, we address these issues by introducing a deep learning model that predicts connectomes based on factor values. The predictions are defined on a simplex spanned across correlation matrices, whose convex combination guarantees that the deep learning model generates well-formed connectomes. We present an efficient method for creating these simplexes and improve the accuracy of the entire analysis by defining loss functions based on robust norms. We show that our deep learning approach is able to produce accurate models on challenging synthetic data. Furthermore, we apply the approach to the resting-state fMRI scans of 281 subjects to study the effect of sex, alcohol, and HIV on brain function.