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Abstract:
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Despite the wide adoption of spike-and-slab methodology for Bayesian variable selection, its potential for penalized likelihood estimation has largely been overlooked. We bridge this gap by cross-fertilizing these two paradigms with the Spike-and-Slab Lasso, a procedure for simultaneous variable selection and parameter estimation in linear regression. A hierarchical mixture of two Laplace distributions, the Spike-and-Slab Lasso prior induces a new class of self-adaptive penalty functions that move beyond the separable penalty framework. A virtue of these non-separable penalties is their ability to borrow strength across coordinates, to adapt to ensemble sparsity information and to exert multiplicity adjustment. Implemented with a path-following optimization scheme for dynamic posterior exploration, the Spike-and-Slab Lasso is seen to mimic oracle performance. Further elaborations of the Spike-and-Slab Lasso for fast Bayesian factor analysis illuminate its broad potential.
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