稀疏 regime 中线性相依协变量下的 Lasso 普适性
Lasso Universality Under Linearly Dependent Covariates in the Sparse Regime
浏览论文内容
中文总结 AI 辅助
本文研究线性相依协变量下的 Lasso 普适性问题，证明了稀疏 regime 中 Lasso 的高斯普适性定理，其相依结构比现有研究更广泛，数值示例验证了该结论。
中文摘要 AI 辅助
过去十年，高斯普适性已被广泛研究用于高维估计问题。多数文献聚焦于独立同分布（i.i.d.）感知矩阵，或考虑特殊形式的相依性，如块相依性或其他特定的行/列相依性，而更一般的行与列同时混合相依性尚未得到充分研究。本文聚焦该场景，证明了稀疏 regime 中 Lasso 的高斯普适性定理，其中非高斯协变量具有线性相依的行与列。据我们所知，本文的场景比多数现有普适性文献所处理的场景允许更广泛的行与列同时相依结构，对各类稀疏性的数值示例支持本文的普适性结论。
英文摘要
Throughout the last decade, Gaussian universality has been widely studied for high-dimensional estimation problems. Most of the literature focuses on i.i.d. sensing matrices or accounts for special forms of dependence, such as block dependence or other specific row/column dependencies. More general simultaneous row and column mixing has not yet been fully studied. In this paper, we focus on that setting. We prove a Gaussian universality theorem for the lasso in the sparse regime, where the non- Gaussian covariates have linearly dependent rows and columns. To the best of our knowledge, our setting permits a broader simultaneous row and column dependence structure than those treated in much of the prior universality literature. Numerical illustrations for various sparse profiles support the universality claims of this paper.
