Connectivity-Informed Adaptive Regularization for Generalized Outcomes

One of the challenging problems in the brain imaging research is a principled incorporation of information from different imaging modalities in association studies. Frequently, data from 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, griPEER (generalized ridgified Partially Empirical Eigenvectors for Regression) to estimate the association between the brain structure features and a scalar outcome within the generalized linear regression framework. griPEER provides a principled approach to use external information from the structural brain connectivity to improve the regression coefficient estimation. Our proposal incorporates a penalty term, derived from the structural connectivity Laplacian matrix, in the penalized generalized linear regression. We address both theoretical and computational issues and show that our method is robust to the incomplete information about the structural brain connectivity. We also provide a significance testing procedure for performing inference on the estimated coefficients in this model. griPEER is evaluated in extensive simulation studies and it is applied in classification of the HIV+ and HIV- individuals.