Phase transition in compressed sensing with horseshoe prior

TL;DR

This paper analyzes the phase transition in compressed sensing when using the horseshoe prior, revealing a broader recoverability phase than traditional methods, through a statistical mechanical approach.

Contribution

It introduces a phase transition analysis for compressed sensing with the horseshoe prior, showing improved recoverability over $l_1$ regularization.

Findings

Existence of a phase transition in signal recoverability.

Recoverability phase is more extensive than with $l_1$ regularization.

Utilizes statistical mechanical methods for analysis.

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.