Reducing subspace dynamic connectivity estimation in MGARCH models for brain health classification

Abstract Functional connectivity (FC) estimation has become a powerful tool for investigating both healthy and abnormal brain function. While traditional resting-state functional Magnetic Resonance Imaging (fMRI) studies have focused on static connectivity, growing evidence reveals that FC exhibits temporal fluctuations, highlighting the need to model FC as a dynamic quantity. In this paper, we propose a novel model that targets a reduced subspace within the covariance structure, enhancing estimation efficiency while preserving key dynamic relationships. The proposed framework is built upon a BEKK-GARCH structure, enabling flexible modeling of time-varying covariance dynamics within a reduced subspace. By leveraging the concept of a Core Subspace (CS), our model captures material information within a specific portion of the covariance matrix, significantly reducing dimensionality without losing essential information. The quasi-maximum likelihood (QML) estimates of the model’s parameters are derived, and their asymptotic properties are established under both normality and nonnormality assumptions. We validate the effectiveness of our approach through simulation studies and apply it to real fMRI data, demonstrating its utility in analyzing and classifying connectivity patterns associated with epilepsy. This framework holds promise for improved FC estimation and dynamic brain health classification.