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Quadratic mixed integer programming and support vectors for deleting outliers in robust regression

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  • G. Zioutas
  • L. Pitsoulis
  • A. Avramidis

Abstract

We consider the problem of deleting bad influential observations (outliers) in linear regression models. The problem is formulated as a Quadratic Mixed Integer Programming (QMIP) problem, where penalty costs for discarding outliers are used into the objective function. The optimum solution defines a robust regression estimator called penalized trimmed squares (PTS). Due to the high computational complexity of the resulting QMIP problem, the proposed robust procedure is computationally suitable for small sample data. The computational performance and the effectiveness of the new procedure are improved significantly by using the idea of ε-Insensitive loss function from support vectors machine regression. Small errors are ignored, and the mathematical formula gains the sparseness property. The good performance of the ε-Insensitive PTS (IPTS) estimator allows identification of multiple outliers avoiding masking or swamping effects. The computational effectiveness and successful outlier detection of the proposed method is demonstrated via simulated experiments. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • G. Zioutas & L. Pitsoulis & A. Avramidis, 2009. "Quadratic mixed integer programming and support vectors for deleting outliers in robust regression," Annals of Operations Research, Springer, vol. 166(1), pages 339-353, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:339-353:10.1007/s10479-008-0412-4
    DOI: 10.1007/s10479-008-0412-4
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    References listed on IDEAS

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    1. Hawkins, Douglas M., 1994. "The feasible solution algorithm for least trimmed squares regression," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 185-196, February.
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    Cited by:

    1. Thompson, Ryan, 2022. "Robust subset selection," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    2. Mike G. Tsionas, 2021. "Multi-criteria optimization in regression," Annals of Operations Research, Springer, vol. 306(1), pages 7-25, November.
    3. Farnè, Matteo & Vouldis, Angelos T., 2018. "A methodology for automised outlier detection in high-dimensional datasets: an application to euro area banks' supervisory data," Working Paper Series 2171, European Central Bank.
    4. Luca Insolia & Ana Kenney & Francesca Chiaromonte & Giovanni Felici, 2022. "Simultaneous feature selection and outlier detection with optimality guarantees," Biometrics, The International Biometric Society, vol. 78(4), pages 1592-1603, December.
    5. C. Chatzinakos & L. Pitsoulis & G. Zioutas, 2016. "Optimization techniques for robust multivariate location and scatter estimation," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1443-1460, May.
    6. Wang, Yong & Fu, Chengqun & Guo, Jie & Yu, Qin, 2016. "A robust regression based on weighted LSSVM and penalized trimmed squaresAuthor-Name: Liu, Jianyong," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 328-334.
    7. Onur Şeref & Talayeh Razzaghi & Petros Xanthopoulos, 2017. "Weighted relaxed support vector machines," Annals of Operations Research, Springer, vol. 249(1), pages 235-271, February.

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