Precise Error Analysis of the LASSO under Correlated Designs
arXiv:2008.13033
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.
References in corpus (7)
- Message Passing Algorithms for Compressed Sensing
- On the Capacity of Doubly Correlated MIMO Channels
- A framework to characterize performance of LASSO algorithms
- The LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements
- Symbol Error Rate Performance of Box-relaxation Decoders in Massive MIMO
- SNR Estimation in Linear Systems with Gaussian Matrices
- Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties