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Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model

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  • J. Brooks
  • Eva Lee

Abstract

Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing “good” two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the “optimal” classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. We investigate properties of a mixed-integer programming based multi-category classification model that allows for the pre-specification of limits on inter-group misclassification rates. The mechanism by which the limits are satisfied is the use of a reserved judgment region, an artificial category into which observations are placed whose attributes do not sufficiently indicate membership to any particular group. The method is shown to be a consistent estimator of a classification rule with misclassification limits, and performance on simulated and real-world data is demonstrated. Copyright Springer Science+Business Media, LLC 2010

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  • J. Brooks & Eva Lee, 2010. "Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model," Annals of Operations Research, Springer, vol. 174(1), pages 147-168, February.
    • Handle: RePEc:spr:annopr:v:174:y:2010:i:1:p:147-168:10.1007/s10479-008-0424-0
    DOI: 10.1007/s10479-008-0424-0
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    References listed on IDEAS

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    1. Richard Gallagher & Eva Lee & David Patterson, 1997. "Constrained discriminant analysis via 0/1 mixed integer programming," Annals of Operations Research, Springer, vol. 74(0), pages 65-88, November.
    2. Eva K. Lee & Richard J. Gallagher & David A. Patterson, 2003. "A Linear Programming Approach to Discriminant Analysis with a Reserved-Judgment Region," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 23-41, February.
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    Cited by:

    1. J. Paul Brooks, 2011. "Support Vector Machines with the Ramp Loss and the Hard Margin Loss," Operations Research, INFORMS, vol. 59(2), pages 467-479, April.
    2. S. Basso & A. Ceselli & A. Tettamanzi, 2020. "Random sampling and machine learning to understand good decompositions," Annals of Operations Research, Springer, vol. 284(2), pages 501-526, January.
    3. Eva K. Lee & Ferdinand Pietz & Bernard Benecke & Jacquelyn Mason & Greg Burel, 2013. "Advancing Public Health and Medical Preparedness with Operations Research," Interfaces, INFORMS, vol. 43(1), pages 79-98, February.
    4. J. Paul Brooks & Eva K. Lee, 2014. "Solving a Multigroup Mixed-Integer Programming-Based Constrained Discrimination Model," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 567-585, August.
    5. Eva K. Lee & Hany Y. Atallah & Michael D. Wright & Eleanor T. Post & Calvin Thomas & Daniel T. Wu & Leon L. Haley, 2015. "Transforming Hospital Emergency Department Workflow and Patient Care," Interfaces, INFORMS, vol. 45(1), pages 58-82, February.
    6. Eva K. Lee & Helder I. Nakaya & Fan Yuan & Troy D. Querec & Greg Burel & Ferdinand H. Pietz & Bernard A. Benecke & Bali Pulendran, 2016. "Machine Learning for Predicting Vaccine Immunogenicity," Interfaces, INFORMS, vol. 46(5), pages 368-390, October.

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