A Survey of L1 Regression

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).