ℓ1-regularized linear regression: Persistence and oracle inequalities

ℓ1-regularized linear regression: Persistence and oracle inequalities (2009)

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by Peter Bartlett , Shahar Mendelson , Joseph Neeman

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@MISC{Bartlett09ℓ1-regularizedlinear,
    author = {Peter Bartlett and Shahar Mendelson and Joseph Neeman},
    title = {ℓ1-regularized linear regression: Persistence and oracle inequalities},
    year = {2009}
}

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Abstract

We study the predictive performance of ℓ1-regularized linear regression, including the case where the number of covariates is substantially larger than the sample size. We introduce a new analysis method that does not require uniformly bounded covariates, an assumption that was often necessary with previous techniques. This technique provides an answer to a conjecture of Greenshtein and Ritov [12] regarding the “persistence ” rate for linear regression and allows us to prove an oracle inequality for the error of the regularized minimizer. 1

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