  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.
