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Optimal decision trees for categorical data via integer programming

Author

Listed:
  • Oktay Günlük

    (Cornell University)

  • Jayant Kalagnanam

    (IBM Research)

  • Minhan Li

    (Lehigh University)

  • Matt Menickelly

    (Argonne National Laboratory)

  • Katya Scheinberg

    (Cornell University)

Abstract

Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a mixed integer programming formulation to construct optimal decision trees of a prespecified size. We take the special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of features) at each node. Our approach can also handle numerical features via thresholding. We show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are tractable with modern solvers.

Suggested Citation

  • Oktay Günlük & Jayant Kalagnanam & Minhan Li & Matt Menickelly & Katya Scheinberg, 2021. "Optimal decision trees for categorical data via integer programming," Journal of Global Optimization, Springer, vol. 81(1), pages 233-260, September.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:1:d:10.1007_s10898-021-01009-y
    DOI: 10.1007/s10898-021-01009-y
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    Cited by:

    1. Sanjay Jain & Jónas Oddur Jónasson & Jean Pauphilet & Kamalini Ramdas, 2023. "Robust combination testing: methods and application to COVID-19 detection," Economics Series Working Papers 1009, University of Oxford, Department of Economics.
    2. Blanquero, Rafael & Carrizosa, Emilio & Molero-Río, Cristina & Morales, Dolores Romero, 2022. "On sparse optimal regression trees," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1045-1054.
    3. Victor Blanco & Alberto Japón & Justo Puerto, 2022. "Robust optimal classification trees under noisy labels," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 155-179, March.
    4. Piccialli, Veronica & Romero Morales, Dolores & Salvatore, Cecilia, 2024. "Supervised feature compression based on counterfactual analysis," European Journal of Operational Research, Elsevier, vol. 317(2), pages 273-285.

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