Precise Error Analysis of the LASSO under Correlated Designs
Statistics Theory
2020-09-18 v2 Information Theory
math.IT
Statistics Theory
Abstract
In this paper, we consider the problem of recovering a sparse signal from noisy linear measurements using the so called LASSO formulation. We assume a correlated Gaussian design matrix with additive Gaussian noise. We precisely analyze the high dimensional asymptotic performance of the LASSO under correlated design matrices using the Convex Gaussian Min-max Theorem (CGMT). We define appropriate performance measures such as the mean-square error (MSE), probability of support recovery, element error rate (EER) and cosine similarity. Numerical simulations are presented to validate the derived theoretical results.
Cite
@article{arxiv.2008.13033,
title = {Precise Error Analysis of the LASSO under Correlated Designs},
author = {Ayed M. Alrashdi and Houssem Sifaou and Abla Kammoun and Mohamed-Slim Alouini and Tareq Y. Al-Naffouri},
journal= {arXiv preprint arXiv:2008.13033},
year = {2020}
}