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Abstract:
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We develop proximal algorithms for Bayesian regularized regression. Proximal algorithms are useful for solving difficult optimization problems with composite objective functions, especially when they involve nonsmooth functions. We develop a fast implementation with our proximal framework and can induce structured sparsity in the coefficients. We apply our methodology to a variety of problems, including signal recovery, nonlinear quantile regression, and variable selection. We compare our procedure with standard computational methods, such as $L_1$ trend filter, spike-and-slab, and the Bayesian bridge.
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