论文标题
在相关设计下对拉索的精确误差分析
Precise Error Analysis of the LASSO under Correlated Designs
论文作者
论文摘要
在本文中，我们考虑了使用所谓的套索公式从嘈杂的线性测量中恢复稀疏信号的问题。我们假设具有加性高斯噪声的相关高斯设计矩阵。我们精确地分析了使用凸高斯Min-Max定理（CGMT）在相关设计矩阵下LASSO的高维渐近性能。我们定义了适当的性能度量，例如均方误差（MSE），支持恢复的概率，元素错误率（EER）和余弦相似性。提出了数值模拟以验证得出的理论结果。
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.
