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...
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| Format: | Article |
| Language: | en_US |
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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 |
| _version_ | 1811088738875342848 |
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| author | Bellini, A. Chernozhukov, Victor V. Wang, Lie |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Bellini, A. Chernozhukov, Victor V. Wang, Lie |
| author_sort | Bellini, A. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:06:46Z |
| format | Article |
| id | mit-1721.1/71663 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:06:46Z |
| publishDate | 2012 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | mit-1721.1/716632024-06-27T19:21:05Z Square-root lasso: pivotal recovery of sparse signals via conic programming Bellini, A. Chernozhukov, Victor V. Wang, Lie Massachusetts Institute of Technology. Department of Economics Massachusetts Institute of Technology. Department of Mathematics Wang, Lie Chernozhukov, Victor V. Wang, Lie 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. 2012-07-17T19:16:04Z 2012-07-17T19:16:04Z 2011-12 2011-06 Article http://purl.org/eprint/type/JournalArticle 1464-3510 0006-3444 http://hdl.handle.net/1721.1/71663 Belloni, A., V. Chernozhukov, and L. Wang. "Square-root lasso: pivotal recovery of sparse signals via conic programming." Biometrika (2011) 98 (4): 791-806. https://orcid.org/0000-0003-3582-8898 https://orcid.org/0000-0002-3250-6714 en_US http://dx.doi.org/10.1093/biomet/asr043 Biometrika Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Oxford University Press MIT web domain |
| spellingShingle | Bellini, A. Chernozhukov, Victor V. Wang, Lie Square-root lasso: pivotal recovery of sparse signals via conic programming |
| title | Square-root lasso: pivotal recovery of sparse signals via conic programming |
| title_full | Square-root lasso: pivotal recovery of sparse signals via conic programming |
| title_fullStr | Square-root lasso: pivotal recovery of sparse signals via conic programming |
| title_full_unstemmed | Square-root lasso: pivotal recovery of sparse signals via conic programming |
| title_short | Square-root lasso: pivotal recovery of sparse signals via conic programming |
| title_sort | square root lasso pivotal recovery of sparse signals via conic programming |
| url | http://hdl.handle.net/1721.1/71663 https://orcid.org/0000-0003-3582-8898 https://orcid.org/0000-0002-3250-6714 |
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