Square-root lasso: pivotal recovery of sparse signals via conic programming
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 p...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Oxford University Press
2012
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| Online Access: | http://hdl.handle.net/1721.1/71663 https://orcid.org/0000-0003-3582-8898 https://orcid.org/0000-0002-3250-6714 |
| Summary: | 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. |
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