Precise Error Analysis of the LASSO under Correlated Designs

Autor: Alrashdi, Ayed M., Sifaou, Houssem, Kammoun, Abla, Alouini, Mohamed-Slim, Al-Naffouri, Tareq Y.
Rok vydání: 2020
Předmět:
Druh dokumentu: Working Paper
Popis: 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.
Databáze: arXiv