Least angle and ${\ell }_1$ penalized regression: A review

Abstract

Least Angle Regression is a promising technique for variable selection applications, offering a nice alternative to stepwise regression. It provides an explanation for the similar behavior of LASSO (${\ell }_1$-penalized regression) and forward stagewise regression, and provides a fast implementation of both. The idea has caught on rapidly, and sparked a great deal of research interest. In this paper, we give an overview of Least Angle Regression and the current state of related research.

Published in at http://dx.doi.org/10.1214/08-SS035 the Statistics Surveys (http://www.i-journals.org/ss/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (7)

• Pathwise coordinate optimization
• On the "degrees of freedom" of the lasso
• One-step sparse estimates in nonconcave penalized likelihood models
• The sparsity and bias of the Lasso selection in high-dimensional linear regression
• Piecewise linear regularized solution paths
• Discussion: One-step sparse estimates in nonconcave penalized likelihood models
• Smoothing ${\ell }_1$-penalized estimators for high-dimensional time-course data