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Classification and Regression via Integer Optimization

Author

Listed:
  • Dimitris Bertsimas

    (Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, E53-363, Cambridge, Massachusetts 02139)

  • Romy Shioda

    (Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1)

Abstract

Motivated by the significant advances in integer optimization in the past decade, we introduce mixed-integer optimization methods to the classical statistical problems of classification and regression and construct a software package called CRIO (classification and regression via integer optimization). CRIO separates data points into different polyhedral regions. In classification each region is assigned a class, while in regression each region has its own distinct regression coefficients. Computational experimentations with generated and real data sets show that CRIO is comparable to and often outperforms the current leading methods in classification and regression. We hope that these results illustrate the potential for significant impact of integer optimization methods on computational statistics and data mining.

Suggested Citation

  • Dimitris Bertsimas & Romy Shioda, 2007. "Classification and Regression via Integer Optimization," Operations Research, INFORMS, vol. 55(2), pages 252-271, April.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:2:p:252-271
    DOI: 10.1287/opre.1060.0360
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    References listed on IDEAS

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    1. O. L. Mangasarian, 1965. "Linear and Nonlinear Separation of Patterns by Linear Programming," Operations Research, INFORMS, vol. 13(3), pages 444-452, June.
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    Cited by:

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    2. Steffen Rebennack & Vitaliy Krasko, 2020. "Piecewise Linear Function Fitting via Mixed-Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 507-530, April.
    3. Benati, Stefano & Puerto, Justo & Rodríguez-Chía, Antonio M., 2017. "Clustering data that are graph connected," European Journal of Operational Research, Elsevier, vol. 261(1), pages 43-53.
    4. Emilio Carrizosa & Vanesa Guerrero & Dolores Romero Morales, 2023. "On mathematical optimization for clustering categories in contingency tables," 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. 17(2), pages 407-429, June.
    5. Emilio Carrizosa & Cristina Molero-Río & Dolores Romero Morales, 2021. "Mathematical optimization in classification and regression trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 5-33, April.
    6. Joki, Kaisa & Bagirov, Adil M. & Karmitsa, Napsu & Mäkelä, Marko M. & Taheri, Sona, 2020. "Clusterwise support vector linear regression," European Journal of Operational Research, Elsevier, vol. 287(1), pages 19-35.
    7. Kraus, Mathias & Feuerriegel, Stefan & Oztekin, Asil, 2020. "Deep learning in business analytics and operations research: Models, applications and managerial implications," European Journal of Operational Research, Elsevier, vol. 281(3), pages 628-641.
    8. Lingxun Kong & Christos T. Maravelias, 2020. "On the Derivation of Continuous Piecewise Linear Approximating Functions," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 531-546, July.
    9. Young Woong Park & Yan Jiang & Diego Klabjan & Loren Williams, 2017. "Algorithms for Generalized Clusterwise Linear Regression," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 301-317, May.
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    12. Liu, Jiapeng & Liao, Xiuwu & Huang, Wei & Yang, Jian-bo, 2018. "A new decision-making approach for multiple criteria sorting with an imbalanced set of assignment examples," European Journal of Operational Research, Elsevier, vol. 265(2), pages 598-620.
    13. Laura Palagi, 2019. "Global optimization issues in deep network regression: an overview," Journal of Global Optimization, Springer, vol. 73(2), pages 239-277, February.
    14. Laura Palagi, 2017. "Global Optimization issues in Supervised Learning. An overview," DIAG Technical Reports 2017-11, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    15. Nguyen, T.D. & Welsch, R., 2010. "Outlier detection and least trimmed squares approximation using semi-definite programming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3212-3226, December.
    16. Brandner, Hubertus & Lessmann, Stefan & Voß, Stefan, 2013. "A memetic approach to construct transductive discrete support vector machines," European Journal of Operational Research, Elsevier, vol. 230(3), pages 581-595.
    17. Yunxiao Deng & Suvrajeet Sen, 2022. "Predictive stochastic programming," Computational Management Science, Springer, vol. 19(1), pages 65-98, January.
    18. Araújo, Paulo H. M. & Campêlo, Manoel & Corrêa, Ricardo C. & Labbé, Martine, 2024. "Integer programming models and polyhedral study for the geodesic classification problem on graphs," European Journal of Operational Research, Elsevier, vol. 314(3), pages 894-911.
    19. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.
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