Predictive sparse modeling of fMRI data for improved classification, regression, and visualization using the k-support norm

We explore various sparse regularization techniques for analyzing fMRI data, such as the ℓ₁ norm (often called LASSO in the context of a squared loss function), elastic net, and the recently introduced k-support norm. Employing sparsity regularization allows us to handle the curse of dimensionality, a problem commonly found in fMRI analysis. In this work we consider sparse regularization in both the regression and classification settings. We perform experiments on fMRI scans from cocaine-addicted as well as healthy control subjects. We show that in many cases, use of the k-support norm leads to better predictive performance, solution stability, and interpretability as compared to other standard approaches. We additionally analyze the advantages of using the absolute loss function versus the standard squared loss which leads to significantly better predictive performance for the regularization methods tested in almost all cases. Our results support the use of the k-support norm for fMRI analysis and on the clinical side, the generalizability of the I-RISA model of cocaine addiction.