Phase transition in compressed sensing with horseshoe prior

Abstract

In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to the sparse estimation. The estimation accuracy of compressed sensing with the horseshoe prior is evaluated by statistical mechanical method. It is found that there exists a phase transition in signal recoverability in the plane of the number of observations and the number of nonzero signals and that the recoverability phase is more extended than that using the well-known $l_1$ norm regularization.

arXiv comment9pages, 5figures

References in corpus (9)

• Nearly unbiased variable selection under minimax concave penalty
• Message Passing Algorithms for Compressed Sensing
• Observed Universality of Phase Transitions in High-Dimensional Geometry, with Implications for Modern Data Analysis and Signal Processing
• A simple sampler for the horseshoe estimator
• Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
• Statistical physics-based reconstruction in compressed sensing
• A typical reconstruction limit of compressed sensing based on Lp-norm minimization
• The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors
• Conditions for Posterior Contraction in the Sparse Normal Means Problem

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