Partially-shared Imaging Regression on Integrating Heterogeneous Brain-Cognition Associations across Alzheimer's Diagnoses

Alzheimer's Disease Neuroimaging Initiative (ADNI) diagnostic groups present strong heterogeneous associations among demographic, imaging, and cognitive data. We propose a novel PArtially-shared Imaging Regression (PAIR) model to represent imaging coefficients as weighted combinations of smooth spatial components. A Total Variation penalty is applied to enforce spatial smoothness, and a Selective Integration penalty is introduced to adaptively learn partial-sharing structures across groups. Theoretically, we establish minimax-optimal error bounds that dynamically adapt to varying sharing paradigms. Numerically, PAIR achieves predictive accuracy comparable to advanced deep learning models while providing superior interpretability. Applied to ADNI data, PAIR reveals substantial heterogeneity in brain-cognition pathways between cognitively normal (CN) and cognitively impaired (CI) groups, with hippocampal imaging contributing minimally in the CN group but substantially in the CI group, particularly in the CA1, CA3, and presubiculum subfields.