Optimal decision trees for categorical data via integer programming

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 pap...

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Veröffentlicht in:Journal of global optimization Jg. 81; H. 1; S. 233 - 260
Hauptverfasser: Günlük, Oktay, Kalagnanam, Jayant, Li, Minhan, Menickelly, Matt, Scheinberg, Katya
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2021
Springer
Springer Nature B.V
Schlagworte:
binary classification
Combinatorial analysis
Computer Science
Decision trees
Integer programming
machine learning
Mathematics
MATHEMATICS AND COMPUTING
Mathematics and Statistics
Mixed integer
Operations Research/Decision Theory
Optimization
Prediction models
Real Functions
Robustness (mathematics)
S.i.: Gerad-40
Integer programming
Decision trees
Binary classification
Machine learning
ISSN:0925-5001, 1573-2916
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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USDOE
National Science Foundation (NSF)
AC02-06CH11357; CCF-1320137
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-021-01009-y