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A robust approach based on conditional value-at-risk measure to statistical learning problems

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  • Takeda, Akiko
  • Kanamori, Takafumi

Abstract

In statistical learning problems, measurement errors in the observed data degrade the reliability of estimation. There exist several approaches to handle those uncertainties in observations. In this paper, we propose to use the conditional value-at-risk (CVaR) measure in order to depress influence of measurement errors, and investigate the relation between the resulting CVaR minimization problems and some existing approaches in the same framework. For the CVaR minimization problems which include the computation of integration, we apply Monte Carlo sampling method and obtain their approximate solutions. The approximation error bound and convergence property of the solution are proved by Vapnik and Chervonenkis theory. Numerical experiments show that the CVaR minimization problem can achieve fairly good estimation results, compared with several support vector machines, in the presence of measurement errors.

Suggested Citation

  • Takeda, Akiko & Kanamori, Takafumi, 2009. "A robust approach based on conditional value-at-risk measure to statistical learning problems," European Journal of Operational Research, Elsevier, vol. 198(1), pages 287-296, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:1:p:287-296
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    References listed on IDEAS

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    1. 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.
    2. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    3. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. Mert Gürbüzbalaban & Andrzej Ruszczyński & Landi Zhu, 2022. "A Stochastic Subgradient Method for Distributionally Robust Non-convex and Non-smooth Learning," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1014-1041, September.
    2. Shivam Gupta & Sachin Modgil & Samadrita Bhattacharyya & Indranil Bose, 2022. "Artificial intelligence for decision support systems in the field of operations research: review and future scope of research," Annals of Operations Research, Springer, vol. 308(1), pages 215-274, January.
    3. Jun-Ya Gotoh & Keita Shinozaki & Akiko Takeda, 2013. "Robust portfolio techniques for mitigating the fragility of CVaR minimization and generalization to coherent risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 13(10), pages 1621-1635, October.
    4. Gao, Fuqing & Wang, Shaochen, 2011. "Asymptotic behavior of the empirical conditional value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 345-352.
    5. Yuichi Takano & Keisuke Nanjo & Noriyoshi Sukegawa & Shinji Mizuno, 2015. "Cutting plane algorithms for mean-CVaR portfolio optimization with nonconvex transaction costs," Computational Management Science, Springer, vol. 12(2), pages 319-340, April.
    6. Rocchetta, Roberto & Crespo, Luis G., 2021. "A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    7. Xu Leiyan & Zhiqing Meng, 2019. "Multi-Loss WCVaR Risk Decision Optimization Based On Weight for Centralized Supply Problem of Direct Chain Enterprises," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-16, April.
    8. Ken Kobayashi & Yuichi Takano & Kazuhide Nakata, 2021. "Bilevel cutting-plane algorithm for cardinality-constrained mean-CVaR portfolio optimization," Journal of Global Optimization, Springer, vol. 81(2), pages 493-528, October.
    9. Ramponi, Federico Alessandro & Campi, Marco C., 2018. "Expected shortfall: Heuristics and certificates," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1003-1013.
    10. Yu, Jing-Rung & Paul Chiou, Wan-Jiun & Hsin, Yi-Ting & Sheu, Her-Jiun, 2022. "Omega portfolio models with floating return threshold," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 743-758.
    11. Zhongde Luo, 2020. "Nonparametric kernel estimation of CVaR under $$\alpha $$α-mixing sequences," Statistical Papers, Springer, vol. 61(2), pages 615-643, April.

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