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Robust chance-constrained support vector machines with second-order moment information

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  • Ximing Wang

    (University of Florida)

  • Neng Fan

    (University of Arizona)

  • Panos M. Pardalos

    (University of Florida)

Abstract

Support vector machines (SVM) is one of the well known supervised classes of learning algorithms. Basic SVM models are dealing with the situation where the exact values of the data points are known. This paper studies SVM when the data points are uncertain. With some properties known for the distributions, chance-constrained SVM is used to ensure the small probability of misclassification for the uncertain data. As infinite number of distributions could have the known properties, the robust chance-constrained SVM requires efficient transformations of the chance constraints to make the problem solvable. In this paper, robust chance-constrained SVM with second-order moment information is studied and we obtain equivalent semidefinite programming and second order cone programming reformulations. The geometric interpretation is presented and numerical experiments are conducted. Three types of estimation errors for mean and covariance information are studied in this paper and the corresponding formulations and techniques to handle these types of errors are presented.

Suggested Citation

  • Ximing Wang & Neng Fan & Panos M. Pardalos, 2018. "Robust chance-constrained support vector machines with second-order moment information," Annals of Operations Research, Springer, vol. 263(1), pages 45-68, April.
    • Handle: RePEc:spr:annopr:v:263:y:2018:i:1:d:10.1007_s10479-015-2039-6
    DOI: 10.1007/s10479-015-2039-6
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    References listed on IDEAS

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    1. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    2. Trafalis, Theodore B. & Gilbert, Robin C., 2006. "Robust classification and regression using support vector machines," European Journal of Operational Research, Elsevier, vol. 173(3), pages 893-909, September.
    3. Keiiti Isii, 1960. "The extrema of probability determined by generalized moments (I) bounded random variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 12(2), pages 119-134, June.
    4. Petros Xanthopoulos & Mario Guarracino & Panos Pardalos, 2014. "Robust generalized eigenvalue classifier with ellipsoidal uncertainty," Annals of Operations Research, Springer, vol. 216(1), pages 327-342, May.
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    Cited by:

    1. Anton Kocheturov & Panos M. Pardalos & Athanasia Karakitsiou, 2019. "Massive datasets and machine learning for computational biomedicine: trends and challenges," Annals of Operations Research, Springer, vol. 276(1), pages 5-34, May.
    2. Byunghoon Kim & Young-Seon Jeong & Myong K. Jeong, 2021. "New multivariate kernel density estimator for uncertain data classification," Annals of Operations Research, Springer, vol. 303(1), pages 413-431, August.
    3. Lin, Fengming & Fang, Shu-Cherng & Fang, Xiaolei & Gao, Zheming & Luo, Jian, 2024. "A distributionally robust chance-constrained kernel-free quadratic surface support vector machine," European Journal of Operational Research, Elsevier, vol. 316(1), pages 46-60.
    4. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.

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