FMRI analysis of cocaine addiction using k-support sparsity

In this paper, we explore various sparse regularization techniques for analyzing fMRI data, such as LASSO, elastic net and the recently introduced k-support norm. Employing sparsity regularization allow us to handle the curse of dimensionality, a problem commonly found in fMRI analysis. We test these methods on real data of both healthy subjects as well as cocaine addicted ones and we show that although LASSO has good prediction, it lacks interpretability since the resulting model is too sparse, and results are highly sensitive to the regularization parameter. We find that we can improve prediction performance over the LASSO using elastic net or the k-support norm, which is a convex relaxation to sparsity with an '2 penalty that is tighter than the elastic net. Elastic net and k-support norm overcome the problem of overly sparse solutions, resulting in both good prediction and interpretable solutions, while the k-support norm gave better prediction performance. Our experimental results support the general applicability of the k-support norm in fMRI analysis, both for prediction performance and interpretability.