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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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    7. 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.
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    16. 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.
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