Regularized Functional Partial Least Squares Regression of Neuroimaging Data

Thanks to the rapid technological advancement across scientific and engineering domains, the acquisition of extensive and complex data has become increasingly feasible. One notable source of such data is Functional Magnetic Resonance Imaging (fMRI), which allows for the observation of brain activity in a dynamic and spatial context. The analysis of fMRI data, which are defined over the complicated geometry of the brain, poses unique challenges and opportunities. The advent of fMRI has significantly impacted neuroscience, allowing researchers to pinpoint brain regions involved in specific cognitive activities. However, the existing statistical methods for Functional Data Analysis are often confined to Euclidean domains. This paper introduces an innovative approach to functional Partial Least Squares regression designed for scalar-on-function regression problems. The use of a differential regularization term to accommodate the functional nature of data makes the proposed model particularly suitable for handling data defined over complex domains.