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Tree regression models using statistical testing and mixed integer programming

Gkioulekas, I; Papageorgiou, LG; (2021) Tree regression models using statistical testing and mixed integer programming. Computers and Industrial Engineering , 153 , Article 107059. 10.1016/j.cie.2020.107059.

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Abstract

Regression analysis is a statistical procedure that fits a mathematical function to a set of data in order to capture the relationship between dependent and independent variables. In tree regression, tree structures are constructed by repeated splits of the input space into two subsets, creating if-then-else rules. Such models are popular in the literature due to their ability to be computed quickly and their simple interpretations. This work introduces a tree regression algorithm that exploits an optimisation model of an existing literature method called Mathematical Programming Tree (MPtree) to optimally split nodes into subsets and applies a statistical test to assess the quality of the partitioning. Additionally, an approach of splitting nodes using multivariate decision rules is explored in this work and compared in terms of performance and computational efficiency. Finally, a novel mathematical model is introduced that performs subset selection on each node in order to select an optimal set of variables to considered for splitting, that improves the computational performance of the proposed algorithm.

Type: Article
Title: Tree regression models using statistical testing and mixed integer programming
DOI: 10.1016/j.cie.2020.107059
Publisher version: https://doi.org/10.1016/j.cie.2020.107059
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Mathematical programming; Regression analysis; Decision trees; Subset selection; Optimisation
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Chemical Engineering
URI: https://discovery.ucl.ac.uk/id/eprint/10123829
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