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A regression tree approach using mathematical programming

Yang, L; Liu, S; Tsoka, S; Papageorgiou, LG; (2017) A regression tree approach using mathematical programming. EXPERT SYSTEMS WITH APPLICATIONS , 78 pp. 347-357. 10.1016/j.eswa.2017.02.013. Green open access

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Abstract

Regression analysis is a machine learning approach that aims to accurately predict the value of continuous output variables from certain independent input variables, via automatic estimation of their latent relationship from data. Tree-based regression models are popular in literature due to their flexibility to model higher order non-linearity and great interpretability. Conventionally, regression tree models are trained in a two-stage procedure, i.e. recursive binary partitioning is employed to produce a tree structure, followed by a pruning process of removing insignificant leaves, with the possibility of assigning multivariate functions to terminal leaves to improve generalisation. This work introduces a novel methodology of node partitioning which, in a single optimisation model, simultaneously performs the two tasks of identifying the break-point of a binary split and assignment of multivariate functions to either leaf, thus leading to an efficient regression tree model. Using six real world benchmark problems, we demonstrate that the proposed method consistently outperforms a number of state-of-the-art regression tree models and methods based on other techniques, with an average improvement of 7–60% on the mean absolute errors (MAE) of the predictions.

Type: Article
Title: A regression tree approach using mathematical programming
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.eswa.2017.02.013
Publisher version: http://dx.doi.org/10.1016/j.eswa.2017.02.013
Additional information: © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Keywords: Science & Technology, Technology, Computer Science, Artificial Intelligence, Engineering, Electrical & Electronic, Operations Research & Management Science, Computer Science, Engineering, Regression analysis, Surrogate model, Regression tree, Mathematical programming, Optimisation, PREDICTING SOIL PROPERTIES, SURROGATE MODELS, CLASSIFICATION, PERFORMANCE
UCL classification: UCL
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/1545708
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