Predicting Phenotypes from Brain Connection Structure
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This article focuses on the problem of predicting a response variable based on a network-valued predictor. Our particular motivation is developing interpretable and accurate predictive models for cognitive traits and neuro-psychiatric disorders based on an individual's brain connection network (connectome). Current methods focus on reducing the complex and high-dimensional brain network into a low-dimensional set of pre-specified features prior to applying standard predictive algorithms. Such methods are sensitive to feature choice and inevitably discard information. We instead propose a nonparametric Bayes class of models that utilize information from the entire adjacency matrix defining connections among brain regions in adaptively defining flexible predictive algorithms, while maintaining interpretability. The proposed Bayesian Connectomics (BaCon) model class utilizes Poisson-Dirichlet processes to detect 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 class and develop efficient algorithms for posterior computation. The resulting methods are shown to outperform existing approaches in simulations and applied to a creative reasoning data set.
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