Mathematical optimization in classification and regression trees

• Emilio Carrizosa ^[1] ; Cristina Molero-Río ^[1] ; Dolores Romero Morales ^[2]
  1. [1] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
  2. [2] Copenhagen Business School

     Copenhagen Business School

     Dinamarca

     
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 29, Nº. 1, 2021, págs. 5-33
• Idioma: inglés
• DOI: 10.1007/s11750-021-00594-1
• Enlaces
  • Texto completo
• Resumen

  • 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.