Incorporating prior information with fused sparse group lasso: Application to prediction of clinical measures from neuroimages

Predicting clinical variables from whole‐brain neuroimages is a high‐dimensional problem that can potentially benefit from feature selection or extraction. Penalized regression is a popular embedded feature selection method for high‐dimensional data. For neuroimaging applications, spatial regularization using the ℓ1 or ℓ2 norm of the image gradient has shown good performance, yielding smooth solutions in spatially contiguous brain regions. Enormous resources have been devoted to establishing structural and functional brain connectivity networks that can be used to define spatially distributed yet related groups of voxels. We propose using the fused sparse group lasso (FSGL) penalty to encourage structured, sparse, and interpretable solutions by incorporating prior information about spatial and group structure among voxels. We present optimization steps for FSGL penalized regression using the alternating direction method of multipliers algorithm. With simulation studies and in application to real functional magnetic resonance imaging data from the Autism Brain Imaging Data Exchange, we demonstrate conditions under which fusion and group penalty terms together outperform either of them alone.