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L1 regularization, or regularization with an L1 penalty, is a popular idea in statistics and machine learning. This paper reviews the concept and application of L1 regularization for regression. It is not our aim to present a comprehensive list of the utilities of the L1 penalty in the regression setting. Rather, we focus on what we believe is the set of most representative uses of this regularization technique, which we describe in some detail. Thus, we deal with a number of L1-regularized methods for linear regression, generalized linear models, and time series analysis. Although this review targets practice rather than theory, we do give some theoretical details about L1-penalized linear regression, usually referred to as the least absolute shrinkage and selection operator (lasso). © 2013 International Statistical Institute.

Original publication

DOI

10.1111/insr.12023

Type

Journal article

Journal

International Statistical Review

Publication Date

01/12/2013

Volume

81

Pages

361 - 387