Linearized alternating direction method of multipliers for sparse group and fused LASSO models

Xinxin Li; Lili Mo; Xiaoming YUAN; Jianzhong Zhang

doi:10.1016/j.csda.2014.05.017

Linearized alternating direction method of multipliers for sparse group and fused LASSO models

Xinxin Li, Lili Mo, Xiaoming YUAN^*, Jianzhong Zhang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

40 Citations (Scopus)

Abstract

The least absolute shrinkage and selection operator (LASSO) has been playing an important role in variable selection and dimensionality reduction for linear regression. In this paper we focus on two general LASSO models: Sparse Group LASSO and Fused LASSO, and apply the linearized alternating direction method of multipliers (LADMM for short) to solve them. The LADMM approach is shown to be a very simple and efficient approach to numerically solve these general LASSO models. We compare it with some benchmark approaches on both synthetic and real datasets.

Original language	English
Pages (from-to)	203-221
Number of pages	19
Journal	Computational Statistics and Data Analysis
Volume	79
DOIs	https://doi.org/10.1016/j.csda.2014.05.017
Publication status	Published - Nov 2014

Scopus Subject Areas

Statistics and Probability
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

User-Defined Keywords

Alternating direction method of multipliers
Convex optimization
Least absolute shrinkage and selection operator
Linear regression
Variable selection

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10.1016/j.csda.2014.05.017

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title = "Linearized alternating direction method of multipliers for sparse group and fused LASSO models",

abstract = "The least absolute shrinkage and selection operator (LASSO) has been playing an important role in variable selection and dimensionality reduction for linear regression. In this paper we focus on two general LASSO models: Sparse Group LASSO and Fused LASSO, and apply the linearized alternating direction method of multipliers (LADMM for short) to solve them. The LADMM approach is shown to be a very simple and efficient approach to numerically solve these general LASSO models. We compare it with some benchmark approaches on both synthetic and real datasets.",

keywords = "Alternating direction method of multipliers, Convex optimization, Least absolute shrinkage and selection operator, Linear regression, Variable selection",

author = "Xinxin Li and Lili Mo and Xiaoming YUAN and Jianzhong Zhang",

note = "Funding Information: The authors are grateful to the anonymous referees for their valuable comments and suggestions which have helped us improve the presentation of this paper greatly. The third author was supported by the General Research Fund from Research Grants Council, University Grants Committee, Hong Kong ( 203712 ).",

year = "2014",

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doi = "10.1016/j.csda.2014.05.017",

language = "English",

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T1 - Linearized alternating direction method of multipliers for sparse group and fused LASSO models

AU - Li, Xinxin

AU - Mo, Lili

AU - YUAN, Xiaoming

AU - Zhang, Jianzhong

N1 - Funding Information: The authors are grateful to the anonymous referees for their valuable comments and suggestions which have helped us improve the presentation of this paper greatly. The third author was supported by the General Research Fund from Research Grants Council, University Grants Committee, Hong Kong ( 203712 ).

PY - 2014/11

Y1 - 2014/11

N2 - The least absolute shrinkage and selection operator (LASSO) has been playing an important role in variable selection and dimensionality reduction for linear regression. In this paper we focus on two general LASSO models: Sparse Group LASSO and Fused LASSO, and apply the linearized alternating direction method of multipliers (LADMM for short) to solve them. The LADMM approach is shown to be a very simple and efficient approach to numerically solve these general LASSO models. We compare it with some benchmark approaches on both synthetic and real datasets.

AB - The least absolute shrinkage and selection operator (LASSO) has been playing an important role in variable selection and dimensionality reduction for linear regression. In this paper we focus on two general LASSO models: Sparse Group LASSO and Fused LASSO, and apply the linearized alternating direction method of multipliers (LADMM for short) to solve them. The LADMM approach is shown to be a very simple and efficient approach to numerically solve these general LASSO models. We compare it with some benchmark approaches on both synthetic and real datasets.

KW - Alternating direction method of multipliers

KW - Convex optimization

KW - Least absolute shrinkage and selection operator

KW - Linear regression

KW - Variable selection

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U2 - 10.1016/j.csda.2014.05.017

DO - 10.1016/j.csda.2014.05.017

M3 - Journal article

AN - SCOPUS:84903161800

SN - 0167-9473

VL - 79

SP - 203

EP - 221

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

ER -

Linearized alternating direction method of multipliers for sparse group and fused LASSO models

Abstract

Scopus Subject Areas

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