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 (`1 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 these 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 on an inhibitory control task given fMRI data from a different task, designed to capture emotionally-salient reward responses. The absolute loss function leads to significantly better predictive performance for both methods in almost all cases and the ksupport 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.