Robust Lasso Regression Using Tukey's Biweight Criterion
The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that the adaptive lasso achieves the oracle property. In this work, we propose an extension of the adaptive lasso named the Tukey-lasso. By using...
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| Published in: | Technometrics Vol. 60; no. 1; pp. 36 - 47 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Alexandria
Taylor & Francis
02.01.2018
American Society for Quality and the American Statistical Association American Society for Quality |
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| ISSN: | 0040-1706, 1537-2723 |
| Online Access: | Get full text |
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| Abstract | The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that the adaptive lasso achieves the oracle property. In this work, we propose an extension of the adaptive lasso named the Tukey-lasso. By using Tukey's biweight criterion, instead of squared loss, the Tukey-lasso is resistant to outliers in both the response and covariates. Importantly, we demonstrate that the Tukey-lasso also enjoys the oracle property. A fast accelerated proximal gradient (APG) algorithm is proposed and implemented for computing the Tukey-lasso. Our extensive simulations show that the Tukey-lasso, implemented with the APG algorithm, achieves very reliable results, including for high-dimensional data where p > n. In the presence of outliers, the Tukey-lasso is shown to offer substantial improvements in performance compared to the adaptive lasso and other robust implementations of the lasso. Real-data examples further demonstrate the utility of the Tukey-lasso. Supplementary materials for this article are available online. |
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| AbstractList | The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty termmean that the adaptive lasso achieves the oracle property. In this work, we propose an extension of the adaptive lasso named the Tukey-lasso. By using Tukey’s biweight criterion, instead of squared loss, the Tukey-lasso is resistant to outliers in both the response and covariates. Importantly, we demonstrate that the Tukey-lasso also enjoys the oracle property. A fast accelerated proximal gradient (APG) algorithm is proposed and implemented for computing the Tukey-lasso. Our extensive simulations show that the Tukey-lasso, implemented with the APG algorithm, achieves very reliable results, including for high-dimensional data where p > n. In the presence of outliers, the Tukey-lasso is shown to offer substantial improvements in performance compared to the adaptive lasso and other robust implementations of the lasso. Real-data examples further demonstrate the utility of the Tukey-lasso. Supplementary materials for this article are available online. The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that the adaptive lasso achieves the oracle property. In this work, we propose an extension of the adaptive lasso named theTukey-lasso. By using Tukey's biweight criterion, instead of squared loss, the Tukey-lasso is resistant to outliers in both the response and covariates. Importantly, we demonstrate that the Tukey-lasso also enjoys the oracle property. A fast accelerated proximal gradient (APG) algorithm is proposed and implemented for computing the Tukey-lasso. Our extensive simulations show that the Tukey-lasso, implemented with the APG algorithm, achieves very reliable results, including for high-dimensional data where p > n. In the presence of outliers, the Tukey-lasso is shown to offer substantial improvements in performance compared to the adaptive lasso and other robust implementations of the lasso. Real-data examples further demonstrate the utility of the Tukey-lasso. Supplementary materials for this article are available online. The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that the adaptive lasso achieves the oracle property. In this work, we propose an extension of the adaptive lasso named the Tukey-lasso. By using Tukey's biweight criterion, instead of squared loss, the Tukey-lasso is resistant to outliers in both the response and covariates. Importantly, we demonstrate that the Tukey-lasso also enjoys the oracle property. A fast accelerated proximal gradient (APG) algorithm is proposed and implemented for computing the Tukey-lasso. Our extensive simulations show that the Tukey-lasso, implemented with the APG algorithm, achieves very reliable results, including for high-dimensional data where p > n. In the presence of outliers, the Tukey-lasso is shown to offer substantial improvements in performance compared to the adaptive lasso and other robust implementations of the lasso. Real-data examples further demonstrate the utility of the Tukey-lasso. Supplementary materials for this article are available online. |
| Author | Welsh, Alan Roberts, Steven Chang, Le |
| Author_xml | – sequence: 1 givenname: Le surname: Chang fullname: Chang, Le email: le.chang@anu.edu.au organization: The Australian National University – sequence: 2 givenname: Steven surname: Roberts fullname: Roberts, Steven organization: The Australian National University – sequence: 3 givenname: Alan surname: Welsh fullname: Welsh, Alan organization: The Australian National University |
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| Snippet | The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that... The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty termmean that... |
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| SubjectTerms | Accelerated proximal gradient algorithm Adaptive lasso Algorithms Computer simulation Criteria Estimating techniques Oracle property Outliers (statistics) Parameter estimation Regression analysis Robust estimation Robustness (mathematics) |
| Title | Robust Lasso Regression Using Tukey's Biweight Criterion |
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