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 requires some type of feature selection or extraction. Penalized regression is a popular embedded feature selection method for high dimensional data. For neuroimaging applications, spatial regularization using the $\ell_1$ or $\ell_2$ norm of the image gradient has shown good performance, yielding smooth solutions in spatially contiguous brain regions. However, recently 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 penalty to encourage structured, sparse, interpretable solutions by incorporating prior information about spatial and group structure among voxels. We present optimization steps for fused sparse group lasso penalized regression using the alternating direction method of multipliers algorithm. With simulation studies and in application to real fMRI data from the Autism Brain Imaging Data Exchange, we demonstrate conditions under which fusion and group penalty terms together outperform either of them alone. Supplementary materials for this article are available online.