A survey of numerical algorithms that can solve the Lasso problems

In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the regression coefficients estimated by the Lasso method. Howe...

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Published in:Wiley interdisciplinary reviews. Computational statistics Vol. 15; no. 4; pp. e1602 - n/a
Main Authors: Zhao, Yujie, Huo, Xiaoming
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.07.2023
Wiley Subscription Services, Inc
Subjects:
Algorithms
Coefficients
Computer applications
convergence rate
Iterative methods
L1 regularization
Lasso
Mathematical models
Numerical methods
Objective function
Optimization
Regression coefficients
Regularization
Statistical analysis
Statistical methods
Statistical models
Trajectory planning
ISSN:1939-5108, 1939-0068
Online Access:Get full text
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Summary:In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the regression coefficients estimated by the Lasso method. However, there lacks a comprehensive review discussing the algorithms to solve the optimization problem in Lasso. In this review, we summarize five representative algorithms to optimize the objective function in Lasso, including iterative shrinkage threshold algorithm (ISTA), fast iterative shrinkage‐thresholding algorithms (FISTA), coordinate gradient descent algorithm (CGDA), smooth L1 algorithm (SLA), and path following algorithm (PFA). Additionally, we also compare their convergence rate, as well as their potential strengths and weakness. This article is categorized under: Statistical Models > Linear Models Algorithms and Computational Methods > Numerical Methods Algorithms and Computational Methods > Computational Complexity A survey of numerical algorithms that can solve the Lasso problems.
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ISSN:1939-5108
1939-0068
DOI:10.1002/wics.1602