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A Survey of L 1 Regression
Author(s) -
Vidaurre Diego,
Bielza Concha,
Larrañaga Pedro
Publication year - 2013
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12023
Subject(s) - regularization (linguistics) , linear regression , lasso (programming language) , regression , mathematics , regression analysis , regression diagnostic , linear model , computer science , statistics , econometrics , artificial intelligence , polynomial regression , world wide web
Summary L 1 regularization, or regularization with an L 1 penalty, is a popular idea in statistics and machine learning. This paper reviews the concept and application of L 1 regularization for regression. It is not our aim to present a comprehensive list of the utilities of the L 1 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 L 1 ‐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 L 1 ‐penalized linear regression, usually referred to as the least absolute shrinkage and selection operator (lasso).