Two-Stage Robust Sparse Gradient Methods for Regression Under Heavy-Tailed Designs
重尾设计下回归的两阶段稳健稀疏梯度方法
We study high-dimensional sparse regression under simultaneous heavy-tailed covariates and noise. Heavy-tailed data affect sparse optimization in two different ways: extreme covariates can destabilize the gradient field during global localization, while heavy-tailed noise limits the final statistical accuracy during local refinement. Motivated by this two-phase structure, we propose two-stage RIGHT, a robust sparse first-order method based on coordinate-wise median-of-means…