A Homotopy Algorithm for the Quantile Regression Lasso and Related Piecewise Linear Problems
| Autor: | Michael R. Osborne, Berwin A. Turlach |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Statistics and Probability
Elastic net regularization Mathematical optimization Computational complexity theory Linear programming Homotopy Feature selection Least squares Piecewise linear function Lasso (statistics) Discrete Mathematics and Combinatorics Applied mathematics Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Journal of Computational and Graphical Statistics. 20:972-987 |
| ISSN: | 1537-2715 1061-8600 |
| DOI: | 10.1198/jcgs.2011.09184 |
| Popis: | We show that the homotopy algorithm of Osborne, Presnell, and Turlach (2000), which has proved such an effective optimal path following method for implementing Tibshirani’s “lasso” for variable selection in least squares estimation problems, can be extended to polyhedral objectives in examples such as the quantile regression lasso. The new algorithm introduces the novel feature that it requires two homotopy sequences involving continuation steps with respect to both the constraint bound and the Lagrange multiplier to be performed consecutively. Performance is illustrated by application to several standard datasets, and these results are compared to calculations made with the original lasso homotopy program. This permits an assessment of the computational complexity to be made both for the new method and for the closely related linear programming post-optimality procedures as these generate essentially identical solution trajectories. This comparison strongly favors the least squares selection method. Howe... |
| Databáze: | OpenAIRE |
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