Abstract:
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Motivated by imaging and other large scale biomedical data, we consider the problem of modeling coefficient homogeneity in high-dimensional regression from a Bayesian setting. In practice, this type of problem commonly arises, for example, in scalar-on-image regression, where imaging predictors may be highly collinear and the number of unique coefficients is far less than the number of pixels or voxels. We propose to model this scenario using hard-thresholded Dirichlet process priors on the regression coefficients, inducing both sparsity and more general coefficient homogeneity. We develop efficient posterior computation algorithms and compare thresholding both Dirichlet process and related kernel stick-breaking priors. The proposed approach provides a compelling alternative to existing frequentist regularization methods since it automatically provides uncertainty measures for sparse and homogeneous structure learning. Finally, we illustrate the proposed method on an analysis of resting-state functional magnetic resonance imaging data in the the Autism Brain Imaging Data Exchange (ABIDE) study.
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