BEST SUBSET SELECTION FOR ELIMINATING MULTICOLLINEARITY

By Ryuta Tamura, Ken Kobayashi, Yuichi Takano, Ryuhei Miyashiro, Kazuhide Nakata, Tomomi Matsui. 2017

47 citations recorded by the source corpus.

This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities to the mixed integer quadratic optimization problem. We also devise a mixed integer semidefinite optimization formulation for best subset selection under the condition number constraint. Computational results demonstrate that our cutting plane algorithm frequently provides solutions of better quality than those obtained using local search algorithms for subset selection. Additionally, subset selection by means of our optimization formulation succeeds when the number of candidate explanatory variables is small.

Subfields: Management Science and Operations Research, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/65e9172833826eaa0240622a059c2561cebba0dc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

1. Joe Naoum-Sawaya
2. Bissan Ghaddar
3. Claudio Gambella

In Numerical Analysis

1. Joe Naoum-Sawaya
2. Bissan Ghaddar
3. Claudio Gambella

In Statistics and Probability

1. Joe Naoum-Sawaya
2. Bissan Ghaddar
3. Claudio Gambella

Citations in the corpus

• Optimization Models for Machine Learning: A Survey (2019, methodology): “To this end, [196] introduces a mixed-integer semidefinite programming formulation to eliminate multicollinearity by bounding the condition number.”