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.

9pages, 5figures

References in corpus (3)

• Nearly unbiased variable selection under minimax concave penalty
• Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
• The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors

Cited by in corpus (3)

• Phase transition in binary compressed sensing based on $L_1$-norm minimization
• A short review on the maximum clique problem algorithms with classical, AI, and quantum methods
• Effect of global shrinkage parameter of horseshoe prior in compressed sensing