Spectral Dependence of Convex Regularization: Fundamental Limits under Right-Rotationally Invariant Designs
凸正则化的谱依赖:右旋转不变设计下的基本极限
We study the fundamental limits of convex-regularized estimation in high-dimensional linear regression with right-rotationally invariant design matrices. We show that the asymptotic risks of convex-penalized least squares estimators are lower bounded by the risk of an approximate message passing algorithm known as Bayes VAMP, and we further characterize when the lower bound is attainable. As a technical ingredient in the proof of our lower bound theorem, we characterize the…