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- W2101984585 abstract "We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the $ell_{2}$-prediction error and the $ell_{1}$-risk of the lasso and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus we can estimate a high-dimensional target vector with an error term similar to the one obtained in a situation where one knows the support of the largest coordinates in advance. Moreover, we show that these design matrices have an explicit restricted eigenvalue. Precisely, they satisfy the restricted eigenvalue assumption and the compatibility condition with an explicit constant. Eventually, we capitalize on the recent construction of unbalanced expander graphs due to Guruswami, Umans, and Vadhan, to provide a deterministic polynomial time construction of these design matrices." @default.
- W2101984585 created "2016-06-24" @default.
- W2101984585 creator A5050991089 @default.
- W2101984585 date "2010-10-12" @default.
- W2101984585 modified "2023-09-23" @default.
- W2101984585 title "Optimal designs for Lasso and Dantzig selector using Expander Codes" @default.
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