Nonparametric Group Variable Selection with Multivariate Response for Connectome-Based Modeling of Cognitive Scores

Abstract

In this article, we study possible relations between the structural connectome and cognitive profiles using a multi-response nonparametric regression model under group sparsity. The aim is to identify the brain regions having significant effect on cognitive functioning. The cognitive profiles are measured in terms of seven cognitive test scores from NIH toolbox of cognitive battery. We consider age-adjusted cognitive scores in this article. The structural connectomes are represented by adjacency matrices. Most existing works consider the upper or lower triangular section of these adjacency matrices as predictors. An alternative characterization of the connectivity properties is available in terms of the nodal attributes. Although any single nodal attribute may not be adequate to represent a complex brain network, a collection of nodal centralities together can encode different patterns of connections in the brain network. In this article, we consider nine different attributes for each brain region as our predictors. Here, each node thus correspond to a collection of nodal attributes. Hence, these nodal graph metrics may naturally be grouped together for each node, motivating us to introduce group sparsity for feature selection. We propose Gaussian RBF-nets with a novel group sparsity inducing prior to model the unknown mean functions. The covariance structure of the multivariate response is characterized in terms of a linear factor modeling framework. For posterior computation, we develop an efficient Markov chain Monte Carlo sampling algorithm. We show that the proposed method performs overwhelmingly better than all its competitors. Applying our proposed method to a Human Connectome Project (HCP) dataset, we identify the important brain regions and nodal attributes for cognitive functioning, as well as identify interesting low-dimensional dependency structures among the cognition related test scores.