  In this paper, we consider voxel selection for functional Magnetic Resonance
Imaging (fMRI) brain data with the aim of finding a more complete set of
probably correlated discriminative voxels, thus improving interpretation of the
discovered potential biomarkers. The main difficulty in doing this is an
extremely high dimensional voxel space and few training samples, resulting in
unreliable feature selection. In order to deal with the difficulty, stability
selection has received a great deal of attention lately, especially due to its
finite sample control of false discoveries and transparent principle for
choosing a proper amount of regularization. However, it fails to make explicit
use of the correlation property or structural information of these
discriminative features and leads to large false negative rates. In other
words, many relevant but probably correlated discriminative voxels are missed.
Thus, we propose a new variant on stability selection "randomized structural
sparsity", which incorporates the idea of structural sparsity. Numerical
experiments demonstrate that our method can be superior in controlling for
false negatives while also keeping the control of false positives inherited
from stability selection.
