Brain connectivity-informed regularization methods for regression

Abstract

A challenging problem arising in brain imaging research is principled incorporation of information from different imaging modalities. Frequently each modality is analyzed separately using, for instance, dimensionality reduction techniques which result in a loss of mutual information. We propose a novel regularization method to estimate the association between the brain structure features and a scalar outcome within the linear regression framework. Our regularization technique provides a principled approach to utilizing external information arising from the structural brain connectivity to inform the estimation of the regression coefficients. Our proposal extends the classical Tikhonov regularization framework by defining a penalty term based on the structural connectivity-derived Laplacian matrix. In the work presented, we address both theoretical and computational issues. The approach is illustrated using simulated data and compared with other penalized regression methods. Finally, we apply our regularization method to study the associations between the alcoholism phenotypes and brain cortical thickness using a diffusion tensor imaging (DTI) derived measure of structural connectivity.