Abstract
In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to compressed sensing. By considering compressed sensing as a randomly correlated many-body problem, statistical mechanics methods can be used to analyze the problem. In this paper, the estimation accuracy of compressed sensing with the horseshoe prior is evaluated by the statistical mechanical methods of random systems. 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 recoverable phase is more extended than that using the well-known l_{1} norm regularization.
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