Least angle and $\ell_1$ penalized regression: A review

TL;DR

This paper reviews Least Angle Regression and its relation to LASSO, highlighting their algorithms, properties, and recent research developments in variable selection.

Contribution

It provides a comprehensive overview of Least Angle Regression, explaining its connection to LASSO and summarizing recent research advances.

Findings

LAR offers an efficient alternative to stepwise regression.

LASSO and forward stagewise regression have similar behaviors.

The paper summarizes recent research on LAR and related methods.

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.