Precise Error Analysis of the LASSO under Correlated Designs

Ayed M. Alrashdi; Houssem Sifaou; Abla Kammoun; Mohamed-Slim Alouini; Tareq Y. Al-Naffouri

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arXiv · 2008.13033

Precise Error Analysis of the LASSO under Correlated Designs

Ayed M. Alrashdi·Houssem Sifaou·Abla Kammoun·Mohamed-Slim Alouini·Tareq Y. Al-Naffouri

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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.

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Ayed M. Alrashdi, Houssem Sifaou, Abla Kammoun, Mohamed-Slim Alouini, Tareq Y. Al-Naffouri. 2020-09-16. Precise Error Analysis of the LASSO under Correlated Designs. https://arxiv.org/abs/2008.13033

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