Square-root lasso: pivotal recovery of sparse signals via conic programming
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Wang_Square root.pdf
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Author(s)
Bellini, A.
Chernozhukov, Victor V.
Wang, Lie
Date Issued
December 2011
Journal
Biometrika
Publisher
Oxford University Press
Citation
Belloni, A., V. Chernozhukov, and L. Wang. "Square-root lasso: pivotal recovery of sparse signals via conic programming." Biometrika (2011) 98 (4): 791-806.
Version
Author's final manuscript
Abstract
We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors p is large, possibly much larger than n, but only s regressors are significant. The method is a modification of the lasso, called the square-root lasso. The method is pivotal in that it neither relies on the knowledge of the standard deviation σ nor does it need to pre-estimate σ. Moreover, the method does not rely on normality or sub-Gaussianity of noise. It achieves near-oracle performance, attaining the convergence rate σ{(s/n) log p}1/2 in the prediction norm, and thus matching the performance of the lasso with known σ. These performance results are valid for both Gaussian and non-Gaussian errors, under some mild moment restrictions. We formulate the square-root lasso as a solution to a convex conic programming problem, which allows us to implement the estimator using efficient algorithmic methods, such as interior-point and first-order methods.
MIT Department
Massachusetts Institute of Technology. Department of Economics
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1093/biomet/asr043
