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In this article, we study association between the structural connectome andcognitive profiles using a multi-response nonparametric regression model.Thecognitive profiles are measured in terms of seven age-adjusted cognitive testscores. The structural connectomes are represented by undirected graphs. Theconnectivity properties of these graphs are available in terms of the nodalattributes. A collection of nodal centralities together can encode differentpatterns of connections in the brain network. In this article, we consider ninesuch attributes for each brain region.These nodal graph metrics may naturallybe grouped together for each node, motivating us to introduce group sparsityfor feature selection. We propose Gaussian RBF-nets with a novel group sparsityinducing prior to model the unknown mean functions. The covariance structure ofthe multivariate response is characterized in terms of a linear factor modelingframework. For posterior computation, we develop an efficient Markov chainMonte Carlo sampling algorithm. We show that the proposed method performs muchbetter than all its competitors. Applying our proposed method to a HumanConnectome Project (HCP) dataset, we identify the important brain regions andnodal attributes for cognitive functioning, as well as identify interestinglow-dimensional dependency structures among the cognition related test scores.Keywords: Factor model; Group variable selection; High-dimension; HumanConnectome Project (HCP); Markov chain Monte Carlo (MCMC); Neural network;Nonparametric inference; Radial basis network; Spike-and-slab prior; Variableselection.

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