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- W4386069324 abstract "This paper introduces a rigorous approach to establish the sharp minimax optimalities of both LASSO and SLOPE within the framework of double sparse structures, notably without relying on RIP-type conditions. Crucially, our findings illuminate that the achievement of these optimalities is fundamentally anchored in a sparse group normalization condition, complemented by several novel sparse group restricted eigenvalue (RE)-type conditions introduced in this study. We further provide a comprehensive comparative analysis of these eigenvalue conditions. Furthermore, we demonstrate that these conditions hold with high probability across a wide range of random matrices. Our exploration extends to encompass the random design, where we prove the random design properties and optimal sample complexity under both weak moment distribution and sub-Gaussian distribution." @default.
- W4386069324 created "2023-08-23" @default.
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- W4386069324 date "2023-08-18" @default.
- W4386069324 modified "2023-09-25" @default.
- W4386069324 title "Sharp minimax optimality of LASSO and SLOPE under double sparsity assumption" @default.
- W4386069324 doi "https://doi.org/10.48550/arxiv.2308.09548" @default.
- W4386069324 hasPublicationYear "2023" @default.
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