  This article focuses on the problem of predicting a response variable based
on a network-valued predictor. Our motivation is the development of
interpretable and accurate predictive models for cognitive traits and
neuro-psychiatric disorders based on an individual's brain connection network
(connectome). Current methods reduce the complex, high dimensional brain
network into low-dimensional pre-specified features prior to applying standard
predictive algorithms. These methods are sensitive to feature choice and
inevitably discard important information. Instead, we propose a nonparametric
Bayes class of models that utilize the entire adjacency matrix defining brain
region connections to adaptively detect predictive algorithms, while
maintaining interpretability. The Bayesian Connectomics (BaCon) model class
utilizes Poisson-Dirichlet processes to find a lower-dimensional, bidirectional
(covariate, subject) pattern in the adjacency matrix. The small n, large p
problem is transformed into a "small n, small q" problem, facilitating an
effective stochastic search of the predictors. A spike-and-slab prior for the
cluster predictors strikes a balance between regression model parsimony and
flexibility, resulting in improved inferences and test case predictions. We
describe basic properties of the BaCon model and develop efficient algorithms
for posterior computation. The resulting methods are found to outperform
existing approaches and applied to a creative reasoning data set.
