IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v329y2026i2p641-652.html

Wasserstein support vector machine: Support vector machines made fair

Author

Listed:
  • Carrizosa, Emilio
  • Halskov, Thomas
  • Romero Morales, Dolores

Abstract

In this paper, a novel model combining Support Vector Machines (SVM) and equity is introduced. Assuming that a group of individuals need to be protected against discrimination, we address the problem of training the classifier by jointly maximizing the classification performance (SVM margin) and equity (closeness between the distribution of the predictions in the protected group and the remaining individuals). Training makes an efficient use of the available information, since the margin is evaluated on individuals for which the class label is known, whereas the equity is measured on individuals for whom we know whether they belong to the protected group or not, and thus their class label is not required. We modify the dual SVM formulation with a penalization of the Wasserstein distance between the empirical distribution of the SVM scores from the two groups. In our approach, predictions are made by reweighting the records, and we show that these weights can be found by training an SVM with a modified kernel. Numerical results are presented on classic benchmark datasets in the Fair Machine Learning literature, where we investigate the tradeoff between accuracy and unfairness for different values of the decision threshold. With a mild penalization of the Wasserstein distance, we can dramatically reduce the unfairness while keeping a similar level of accuracy.

Suggested Citation

  • Carrizosa, Emilio & Halskov, Thomas & Romero Morales, Dolores, 2026. "Wasserstein support vector machine: Support vector machines made fair," European Journal of Operational Research, Elsevier, vol. 329(2), pages 641-652.
  • Handle: RePEc:eee:ejores:v:329:y:2026:i:2:p:641-652
    DOI: 10.1016/j.ejor.2025.10.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221725008586
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2025.10.038?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Gah-Yi Ban & Cynthia Rudin, 2019. "The Big Data Newsvendor: Practical Insights from Machine Learning," Operations Research, INFORMS, vol. 67(1), pages 90-108, January.
    2. Carrizosa, Emilio & Kurishchenko, Kseniia & Romero Morales, Dolores, 2025. "On enhancing the explainability and fairness of tree ensembles," European Journal of Operational Research, Elsevier, vol. 323(2), pages 599-608.
    3. Maggioni, Francesca & Spinelli, Andrea, 2025. "A novel robust optimization model for nonlinear Support Vector Machine," European Journal of Operational Research, Elsevier, vol. 322(1), pages 237-253.
    4. Suyun Liu & Luis Nunes Vicente, 2022. "Accuracy and fairness trade-offs in machine learning: a stochastic multi-objective approach," Computational Management Science, Springer, vol. 19(3), pages 513-537, July.
    5. 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.
    6. Blanquero, Rafael & Carrizosa, Emilio & Molero-Río, Cristina & Morales, Dolores Romero, 2022. "On sparse optimal regression trees," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1045-1054.
    7. 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.
    8. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    9. Dimitris Bertsimas & Jean Pauphilet & Jennifer Stevens & Manu Tandon, 2022. "Predicting Inpatient Flow at a Major Hospital Using Interpretable Analytics," Manufacturing & Service Operations Management, INFORMS, vol. 24(6), pages 2809-2824, November.
    10. Véronique Van Vlasselaer & Tina Eliassi-Rad & Leman Akoglu & Monique Snoeck & Bart Baesens, 2017. "GOTCHA! Network-Based Fraud Detection for Social Security Fraud," Management Science, INFORMS, vol. 63(9), pages 3090-3110, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emilio Carrizosa & Cristina Molero-Río & Dolores Romero Morales, 2021. "Mathematical optimization in classification and regression trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 5-33, April.
    2. Baldomero-Naranjo, Marta & Martínez-Merino, Luisa I. & Rodríguez-Chía, Antonio M., 2020. "Tightening big Ms in integer programming formulations for support vector machines with ramp loss," European Journal of Operational Research, Elsevier, vol. 286(1), pages 84-100.
    3. Xi Chen & Zachary Owen & Clark Pixton & David Simchi-Levi, 2022. "A Statistical Learning Approach to Personalization in Revenue Management," Management Science, INFORMS, vol. 68(3), pages 1923-1937, March.
    4. Serrano, Breno & Minner, Stefan & Schiffer, Maximilian & Vidal, Thibaut, 2024. "Bilevel optimization for feature selection in the data-driven newsvendor problem," European Journal of Operational Research, Elsevier, vol. 315(2), pages 703-714.
    5. Wang, Deshen & Chen, Bintong & Chen, Jing, 2019. "Credit card fraud detection strategies with consumer incentives," Omega, Elsevier, vol. 88(C), pages 179-195.
    6. Meng Qi & Ying Cao & Zuo-Jun (Max) Shen, 2022. "Distributionally Robust Conditional Quantile Prediction with Fixed Design," Management Science, INFORMS, vol. 68(3), pages 1639-1658, March.
    7. Jian Luo & Shu-Cherng Fang & Zhibin Deng & Xiaoling Guo, 2016. "Soft Quadratic Surface Support Vector Machine for Binary Classification," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-22, December.
    8. João M. C. Sousa & Rodrigo Luís & Rui Mirra Santos & Luís Mendonça & Susana M. Vieira, 2024. "Fuzzy Multi-Item Newsvendor Problem: An Application to Inventory Management," Mathematics, MDPI, vol. 12(11), pages 1-17, May.
    9. Soham Ghosh & Sujay Mukhoti, 2023. "Non-parametric generalised newsvendor model," Annals of Operations Research, Springer, vol. 321(1), pages 241-266, February.
    10. Jaime D. Acevedo-Viloria & Luisa Roa & Soji Adeshina & Cesar Charalla Olazo & Andr'es Rodr'iguez-Rey & Jose Alberto Ramos & Alejandro Correa-Bahnsen, 2021. "Relational Graph Neural Networks for Fraud Detection in a Super-App environment," Papers 2107.13673, arXiv.org, revised Jul 2021.
    11. Liu, Congzheng & Letchford, Adam N. & Svetunkov, Ivan, 2022. "Newsvendor problems: An integrated method for estimation and optimisation," European Journal of Operational Research, Elsevier, vol. 300(2), pages 590-601.
    12. Schmidt, Felix G. & Pibernik, Richard, 2025. "Data-driven inventory control for large product portfolios: A practical application of prescriptive analytics," European Journal of Operational Research, Elsevier, vol. 322(1), pages 254-269.
    13. Corredera, Alberto & Ruiz, Carlos, 2023. "Prescriptive selection of machine learning hyperparameters with applications in power markets: Retailer’s optimal trading," European Journal of Operational Research, Elsevier, vol. 306(1), pages 370-388.
    14. Wang, Wanpeng & Deng, Shiming & Zhang, Yuying, 2025. "Data-driven ordering policies for target oriented newsvendor with censored demand," European Journal of Operational Research, Elsevier, vol. 323(1), pages 86-96.
    15. Astorino, Annabella & Avolio, Matteo & Fuduli, Antonio, 2022. "A maximum-margin multisphere approach for binary Multiple Instance Learning," European Journal of Operational Research, Elsevier, vol. 299(2), pages 642-652.
    16. Shuaian Wang & Xuecheng Tian, 2023. "A Deficiency of the Predict-Then-Optimize Framework: Decreased Decision Quality with Increased Data Size," Mathematics, MDPI, vol. 11(15), pages 1-9, July.
    17. Sandra Benítez-Peña & Rafael Blanquero & Emilio Carrizosa & Pepa Ramírez-Cobo, 2019. "On support vector machines under a multiple-cost scenario," 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. 13(3), pages 663-682, September.
    18. Carrizosa, Emilio & Ramírez-Ayerbe, Jasone & Romero Morales, Dolores, 2024. "Mathematical optimization modelling for group counterfactual explanations," European Journal of Operational Research, Elsevier, vol. 319(2), pages 399-412.
    19. Blanquero, R. & Carrizosa, E. & Jiménez-Cordero, A. & Martín-Barragán, B., 2019. "Functional-bandwidth kernel for Support Vector Machine with Functional Data: An alternating optimization algorithm," European Journal of Operational Research, Elsevier, vol. 275(1), pages 195-207.
    20. Huirong Zhang & Zhenyu Zhang & Lixin Zhou & Shuangsheng Wu, 2021. "Case-Based Reasoning for Hidden Property Analysis of Judgment Debtors," Mathematics, MDPI, vol. 9(13), pages 1-17, July.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:329:y:2026:i:2:p:641-652. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.