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

In this article, we study association between the structural connectome and cognitive profiles using a multi-response nonparametric regression model.The cognitive profiles are measured in terms of seven age-adjusted cognitive test scores. The structural connectomes are represented by undirected graphs. The connectivity properties of these graphs are available in terms of the nodal attributes. A collection of nodal centralities together can encode different patterns of connections in the brain network. In this article, we consider nine such attributes for each brain region.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 much 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. Keywords: Factor model; Group variable selection; High-dimension; Human Connectome Project (HCP); Markov chain Monte Carlo (MCMC); Neural network; Nonparametric inference; Radial basis network; Spike-and-slab prior; Variable selection.