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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| Published in | Journal of global optimization Vol. 81; no. 1; pp. 233 - 260 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.09.2021
Springer Springer Nature B.V |
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| 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. |
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| AbstractList | 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. 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. Here 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. |
| Audience | Academic |
| Author | Günlük, Oktay Kalagnanam, Jayant Menickelly, Matt Li, Minhan Scheinberg, Katya |
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| BackLink | https://www.osti.gov/servlets/purl/1839906$$D View this record in Osti.gov |
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| Cites_doi | 10.1287/opre.1060.0360 10.1023/A:1010933404324 10.1145/1961189.1961199 10.1007/s10462-011-9272-4 10.1007/s10994-017-5633-9 10.1016/0020-0190(76)90095-8 |
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| References_xml | – reference: Therneau, T., Atkinson, B., Ripley, B.: rpart: Recursive partitioning and regression trees. Technical Report (2017). R package version 4.1-11 – reference: Malioutov, D.M., Varshney, K.R.: Exact rule learning via boolean compressed sensing. In: Proceedings of the 30th International Conference on Machine Learning, volume 3, pp. 765–773 (2013) – reference: ChangCCLinCJLIBSVM: a library for support vector machinesACM Trans. Intell. Syst. Technol.2011227:127:2710.1145/1961189.1961199 – reference: WangTRudinCDoshi-VelezFLiuYKlampflEMacNeillePA Bayesian framework for learning rule sets for interpretable classificationJ. Mach. Learn. Res.2017187013737142331434.68467 – reference: BennettKPBlueJAA support vector machine approach to decision treesNeural Netw. Proc. IEEE World Congr. Comput. Intell.1998323962401 – reference: BertsimasDShiodaRClassification and regression via integer optimizationOper. Res.2017552252271231625810.1287/opre.1060.0360 – reference: KotsiantisSBDecision trees: a recent overviewArtif. Intell. Rev.201339426128310.1007/s10462-011-9272-4 – reference: Murthy, S., Salzberg, S.: Lookahead and pathology in decision tree induction. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence, volume 2, pp. 1025–1031, San Francisco, CA, USA, (1995). Morgan Kaufmann Publishers Inc – reference: Norouzi, M., Collins, M., Johnson, M.A., Fleet, D.J., Kohli, P.: Efficient non-greedy optimization of decision trees. In: Advances in Neural Information Processing Systems, pp. 1720–1728, (2015) – reference: HyafilLRivestRLConstructing optimal binary decision trees is np-completeInform. Process. Lett.197651151741359810.1016/0020-0190(76)90095-8 – reference: Bennett, K.P., Blue, J.: Optimal decision trees. Technical Report 214, Rensselaer Polytechnic Institute Math Report (1996) – reference: BertsimasDDunnJOptimal classification treesMach. Learn.2017106710391082366578810.1007/s10994-017-5633-9 – reference: Wang, T., Rudin, C.: Learning optimized or’s of and’s. Technical report, (2015). arxiv:1511.02210 – reference: FICO Explainable Machine Learning Challenge https://community.fico.com/s/explainable-machine-learning-challenge – reference: BreimanLRandom forestsMach. Learn.200145153210.1023/A:1010933404324 – reference: DashSGünlükOWeiDBoolean Decision Rules via Column Generation. Advances in Neural Information Processing Systems2018CanadaMontreal – reference: BreimanLFriedmanJHOlshenRAStoneCJClassification and Regression Trees1984New YorkChapman and Hall0541.62042 – reference: Lichman, M.: UCI machine learning repository (2013) – reference: RossJQuinlan. C4.5: Programs for Machine Learning1993San FranciscoMorgan Kaufmann Publishers Inc. – volume-title: Classification and Regression Trees year: 1984 ident: 1009_CR5 – volume: 55 start-page: 252 issue: 2 year: 2017 ident: 1009_CR4 publication-title: Oper. Res. doi: 10.1287/opre.1060.0360 – volume-title: Quinlan. C4.5: Programs for Machine Learning year: 1993 ident: 1009_CR16 – ident: 1009_CR9 – volume-title: Boolean Decision Rules via Column Generation. Advances in Neural Information Processing Systems year: 2018 ident: 1009_CR8 – volume: 3 start-page: 2396 year: 1998 ident: 1009_CR2 publication-title: Neural Netw. Proc. IEEE World Congr. Comput. Intell. – volume: 45 start-page: 5 issue: 1 year: 2001 ident: 1009_CR6 publication-title: Mach. Learn. doi: 10.1023/A:1010933404324 – volume: 2 start-page: 27:1 year: 2011 ident: 1009_CR7 publication-title: ACM Trans. Intell. Syst. Technol. doi: 10.1145/1961189.1961199 – ident: 1009_CR1 – volume: 39 start-page: 261 issue: 4 year: 2013 ident: 1009_CR11 publication-title: Artif. Intell. Rev. doi: 10.1007/s10462-011-9272-4 – volume: 106 start-page: 1039 issue: 7 year: 2017 ident: 1009_CR3 publication-title: Mach. Learn. doi: 10.1007/s10994-017-5633-9 – volume: 18 start-page: 1 issue: 70 year: 2017 ident: 1009_CR19 publication-title: J. Mach. Learn. Res. – ident: 1009_CR15 – ident: 1009_CR17 – volume: 5 start-page: 15 issue: 1 year: 1976 ident: 1009_CR10 publication-title: Inform. Process. Lett. doi: 10.1016/0020-0190(76)90095-8 – ident: 1009_CR13 – ident: 1009_CR18 – ident: 1009_CR14 – ident: 1009_CR12 |
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| Title | Optimal decision trees for categorical data via integer programming |
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