On Sparse Optimal Regression Trees

Rafael Blanquero, Emilio Carrizosa, Cristina Molero-Río*, Dolores Romero Morales

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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In this paper, we model an optimal regression tree through a continuous optimization problem, where a compromise between prediction accuracy and both types of sparsity, namely local and global, is sought. Our approach can accommodate important desirable properties for the regression task, such as cost-sensitivity and fairness. Thanks to the smoothness of the predictions, we can derive local explanations on the continuous predictor variables. The computational experience reported shows the outperformance of our approach in terms of prediction accuracy against standard benchmark regression methods such as CART, OLS and LASSO. Moreover, the scalability of our approach with respect to the size of the training sample is illustrated.
Original languageEnglish
JournalEuropean Journal of Operational Research
Issue number3
Pages (from-to)1045-1054
Number of pages10
Publication statusPublished - Jun 2022


  • Machine learning
  • Classification and regression trees
  • Optimal regression trees
  • Sparsity
  • Nonlinear programming

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