Predicting cross-task behavioral variables from fMRI data using the k-support norm

Sparsity regularization allows handling the curse of dimensionality, a problem commonly found in fMRI data. In this paper, we compare LASSO (L1 regularization) and the recently introduced k-support norm on their ability to predict real valued variables from brain fMRI data for cocaine addiction, in a principled model selection setting. Furthermore, in the context of those two regularization methods, we compare two loss functions: squared loss and absolute loss. With the squared loss function, k-support norm outperforms LASSO in predicting real valued behavioral variables measured in an inhibitory control task given fMRI data from a different task, designed to capture emotionally-salient reward. The absolute loss function leads to significantly better predictive performance for both methods in almost all cases and the k-support norm leads to more interpretable and more stable solutions often by an order of magnitude. Our results support the use of the k-support norm for fMRI analysis and the generalizability of the I-RISA model of cocaine addiction.