Precise Error Analysis of the LASSO under Correlated Designs

2020/08/29 by Ayed M. Alrashdi, Alrashdi, Ayed M., Houssem Sifaou +8
Computer Science · Engineering · Mathematics · #Blind Source Separation Techniques #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #cs.IT #math.IT #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.2008.13033

openalex publication_date 2020/08/29 · arxiv created 2020/09/16 · arxiv updated 2020/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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.

Citations

• The LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements
• A framework to characterize performance of LASSO algorithms
• Joint Spatial Division and Multiplexing—The Large-Scale Array Regime

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