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In many problem settings, parameter vectors are not merely sparse butdependent in such a way that non-zero coefficients tend to cluster together. Werefer to this form of dependency as "region sparsity." Classical sparseregression methods, such as the lasso and automatic relevance determination(ARD), which model parameters as independent a priori, and therefore do notexploit such dependencies. Here we introduce a hierarchical model for smooth,region-sparse weight vectors and tensors in a linear regression setting. Ourapproach represents a hierarchical extension of the relevance determinationframework, where we add a transformed Gaussian process to model thedependencies between the prior variances of regression weights. We combine thiswith a structured model of the prior variances of Fourier coefficients, whicheliminates unnecessary high frequencies. The resulting prior encourages weightsto be region-sparse in two different bases simultaneously. We develop Laplaceapproximation and Monte Carlo Markov Chain (MCMC) sampling to provide efficientinference for the posterior. Furthermore, a two-stage convex relaxation of theLaplace approximation approach is also provided to relax the inevitablenon-convexity during the optimization. We finally show substantial improvementsover comparable methods for both simulated and real datasets from brainimaging.

Dependent relevance determination for smooth and structured sparse regression