Least angle and ℓ1 penalized regression: A review

2008/01/01 by Tim Hesterberg, Nam Hee Choi, Lukas Meier +1 · 1 citation
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Machine Learning and ELM #Statistical Methods and Inference #msc:62J07 #msc:69J99 #stat.ME #stat.ML

paper · pdf · doi:10.1214/08-ss035

published as Statistics Surveys 2008, Vol. 2, 61-93 · 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)

openalex publication_date 2008/01/01 · arxiv created 2008/05/21 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05

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 (ℓ1-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.

Citations

• Sparse Principal Component Analysis
• Atomic Decomposition by Basis Pursuit
• A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting
• Least angle regression
• A Statistical View of Some Chemometrics Regression Tools
• Multivariate Adaptive Regression Splines
• Large-Scale Bayesian Logistic Regression for Text Categorization
• Discussion: One-step sparse estimates in nonconcave penalized likelihood models
• One-step sparse estimates in nonconcave penalized likelihood models
• Piecewise linear regularized solution paths
• The Group Lasso for Logistic Regression
• The sparsity and bias of the Lasso selection in high-dimensional linear regression

Cited by

• Tim Hesterberg [wikipedia]

Related

• Least angle regression
• Least Angle Regression and LASSO for Large Datasets
• LASSO regression
• Solar: L₀ solution path averaging for fast and accurate variable selection in high-dimensional data
• Exact Post-Selection Inference for Sequential Regression Procedures