Choosing the best set of variables in regression analysis using integer programming

Hiroshi Konno; Rei Yamamoto

doi:10.1007/s10898-008-9323-9

Choosing the best set of variables in regression analysis using integer programming

Hiroshi Konno, Rei Yamamoto

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

This paper is concerned with an algorithm for selecting the best set of s variables out of k(> s) candidate variables in a multiple linear regression model. We employ absolute deviation as the measure of deviation and solve the resulting optimization problem by using 0-1 integer programming methodologies. In addition, we will propose a heuristic algorithm to obtain a close to optimal set of variables in terms of squared deviation. Computational results show that this method is practical and reliable for determining the best set of variables.

Original language	English
Pages (from-to)	273-282
Number of pages	10
Journal	Journal of Global Optimization
Volume	44
Issue number	2
DOIs	https://doi.org/10.1007/s10898-008-9323-9
Publication status	Published - 2009 Jun
Externally published	Yes

Keywords

0-1 integer programming
Cardinality constraint
Least absolute deviation
Linear regression
Variable selection

ASJC Scopus subject areas

Computer Science Applications
Management Science and Operations Research
Control and Optimization
Applied Mathematics

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10.1007/s10898-008-9323-9

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abstract = "This paper is concerned with an algorithm for selecting the best set of s variables out of k(> s) candidate variables in a multiple linear regression model. We employ absolute deviation as the measure of deviation and solve the resulting optimization problem by using 0-1 integer programming methodologies. In addition, we will propose a heuristic algorithm to obtain a close to optimal set of variables in terms of squared deviation. Computational results show that this method is practical and reliable for determining the best set of variables.",

keywords = "0-1 integer programming, Cardinality constraint, Least absolute deviation, Linear regression, Variable selection",

author = "Hiroshi Konno and Rei Yamamoto",

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AU - Yamamoto, Rei

N1 - Funding Information: Acknowledgements The research of the first author has been partly supported by the Grant-in-Aid for Scientific Research B18310109 of MEXT of the Government of Japan.

PY - 2009/6

Y1 - 2009/6

N2 - This paper is concerned with an algorithm for selecting the best set of s variables out of k(> s) candidate variables in a multiple linear regression model. We employ absolute deviation as the measure of deviation and solve the resulting optimization problem by using 0-1 integer programming methodologies. In addition, we will propose a heuristic algorithm to obtain a close to optimal set of variables in terms of squared deviation. Computational results show that this method is practical and reliable for determining the best set of variables.

AB - This paper is concerned with an algorithm for selecting the best set of s variables out of k(> s) candidate variables in a multiple linear regression model. We employ absolute deviation as the measure of deviation and solve the resulting optimization problem by using 0-1 integer programming methodologies. In addition, we will propose a heuristic algorithm to obtain a close to optimal set of variables in terms of squared deviation. Computational results show that this method is practical and reliable for determining the best set of variables.

KW - 0-1 integer programming

KW - Cardinality constraint

KW - Least absolute deviation

KW - Linear regression

KW - Variable selection

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Choosing the best set of variables in regression analysis using integer programming

Abstract

Keywords

ASJC Scopus subject areas

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