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Sparse Linear Regression and Lattice Problems
Feb. 23, 2024, 5:42 a.m. | Aparna Gupte, Neekon Vafa, Vinod Vaikuntanathan
cs.LG updates on arXiv.org arxiv.org
Abstract: Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq k$) and small, arbitrary noise $w$, and the goal is to find a $k$-sparse $\widehat{\theta} \in \mathbb{R}^n$ that minimizes the mean squared prediction error $\frac{1}{m}\|X\widehat{\theta}-X\theta^*\|^2_2$. While $\ell_1$-relaxation methods such as basis pursuit, Lasso, and the Dantzig selector solve SLR when the design matrix …
abstract arxiv cs.lg design lattice linear linear regression matrix noise regression small statistics stat.ml type vector
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