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Mathematical optimization in classification and regression trees

Emilio Carrizosa (), Cristina Molero-Río () and Dolores Romero Morales ()
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Emilio Carrizosa: Instituto de Matemáticas de la Universidad de Sevilla
Cristina Molero-Río: Instituto de Matemáticas de la Universidad de Sevilla
Dolores Romero Morales: Copenhagen Business School

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 29, issue 1, No 2, 5-33

Abstract: Abstract Classification and regression trees, as well as their variants, are off-the-shelf methods in Machine Learning. In this paper, we review recent contributions within the Continuous Optimization and the Mixed-Integer Linear Optimization paradigms to develop novel formulations in this research area. We compare those in terms of the nature of the decision variables and the constraints required, as well as the optimization algorithms proposed. We illustrate how these powerful formulations enhance the flexibility of tree models, being better suited to incorporate desirable properties such as cost-sensitivity, explainability, and fairness, and to deal with complex data, such as functional data.

Keywords: Classification and regression trees; Tree ensembles; Mixed-integer linear optimization; Continuous nonlinear optimization; Sparsity; Explainability; 90C11; 90C30; 62-07 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11750-021-00594-1

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TOP: An Official Journal of the Spanish Society of Statistics and Operations Research is currently edited by Juan José Salazar González and Gustavo Bergantiños

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