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info.json
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{
"abstract": "In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as ``region sparsity.'' Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), which model parameters as independent a priori, and therefore do not exploit such dependencies. Here we introduce a hierarchical model for smooth, region-sparse weight vectors and tensors in a linear regression setting. Our approach represents a hierarchical extension of the relevance determination framework, where we add a transformed Gaussian process to model the dependencies between the prior variances of regression weights. We combine this with a structured model of the prior variances of Fourier coefficients, which eliminates unnecessary high frequencies. The resulting prior encourages weights to be region-sparse in two different bases simultaneously. We develop Laplace approximation and Monte Carlo Markov Chain (MCMC) sampling to provide efficient inference for the posterior. Furthermore, a two-stage convex relaxation of the Laplace approximation approach is also provided to relax the inevitable non-convexity during the optimization. We finally show substantial improvements over comparable methods for both simulated and real datasets from brain imaging.",
"authors": [
"Anqi Wu",
"Oluwasanmi Koyejo",
"Jonathan Pillow"
],
"emails": [
"anqiw@princeton.edu",
"sanmi@illinois.edu",
"pillow@princeton.edu"
],
"id": "17-757",
"issue": 89,
"pages": [
1,
43
],
"title": "Dependent relevance determination for smooth and structured sparse regression",
"volume": 20,
"year": 2019
}