Sharp convergence rate of the estimation error of LASSO via the Feature Space Decomposition method

Abstract

In this paper, we use the Feature Space Decomposition (FSD) method to establish an explicit, non-asymptotic, instance-optimal convergence rate for the estimation error of the LASSO in the Gaussian linear regression problem for any signal, any diagonal covariance and any regularization parameter above ${\sigma }_{\xi }/\sqrt{N}$ where ${\sigma }_{\xi }$ is the noise variance and $N$ the number of data.