Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Stable Anatomy Detection in Multimodal Imaging Through Sparse Group Regularization: A Comparative Study of Iron Accumulation in the Aging Brain

Multimodal neuroimaging provides a rich source of data for identifying brain regions associated with disease progression and aging. However, present studies still typically analyze modalities separately or aggregate voxel-wise measurements and analyses to the structural level, thus reducing statistical power. As a central example, previous works have used two quantitative MRI parameters-R2* and quantitative susceptibility (QS)-to study changes in iron associated with aging in healthy and multiple sclerosis subjects, but failed to simultaneously account for both. In this article, we propose a unified framework that combines information from multiple imaging modalities and regularizes estimates for increased interpretability, generalizability, and stability. Our work focuses on joint region detection problems where overlap between effect supports across modalities is encouraged but not strictly enforced. To achieve this, we combine L ₁ (lasso), total variation (TV), and L ₂ group lasso penalties. While the TV penalty encourages geometric regularization by controlling estimate variability and support boundary geometry, the group lasso penalty accounts for similarities in the support between imaging modalities. We address the computational difficulty in this regularization scheme with an alternating direction method of multipliers (ADMM) optimizer. In a neuroimaging application, we compare our method against independent sparse and joint sparse models using a dataset of R2* and QS maps derived from MRI scans of 113 healthy controls: our method produces clinically-interpretable regions where specific iron changes are associated with healthy aging. Together with results across multiple simulation studies, we conclude that our approach identifies regions that are more strongly associated with the variable of interest (e.g., age), more accurate, and more stable with respect to training data variability. This work makes progress toward a stable and interpretable multimodal imaging analysis framework for studying disease-related changes in brain structure and can be extended for classification and disease prediction tasks.