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Thresholded Lasso for high dimensional variable selection
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AI
DOI：10.1007/s10463-025-00969-2.png)
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Abstract
En 中文
Given n noisy samples with p dimensions, where n << p , we show that the multi-step thresholding procedure based on the Lasso - we call it the Thresholded Lasso, can accurately estimate a sparse vector beta is an element of & Ropf;(p) in a linear model Y = X beta + & varepsilon; , where Xis a design matrix and & varepsilon; similar to N(0, sigma I-2(n)) . Here I-n denotes the identity matrix. We show that under the restricted eigenvalue condition, it is possible to achieve the & lscr;(2) loss within a logarithmic factor of the ideal mean square error one would achieve with an oracle while selecting a sufficiently sparse model - hence achieving sparse oracle inequalities; the oracle would supply perfect information about which coordinates are non-zero and which are above the noise level. We also show the same prop-erty holds for the Gauss-Dantzig selector under a uniform uncertainty principle. Our simulation results match our theoretical analysis excellently.
Keywords:
Lasso
Gauss-Dantzig Selector
& ell
(1)
ideal model selection
oracle inequalities
restricted orthonormality
Restricted Eigenvalue condition
thresholding
random matrices
Journal
A
IF:
0.6
Papers:
26
Citations:
2.1K
