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Support Vector Machines

Author

Listed:
  • Yoann Pull

    (LEO - Laboratoire d'Économie d'Orleans [2022-...] - UO - Université d'Orléans - UT - Université de Tours - UCA - Université Clermont Auvergne)

Abstract

This lecture note offers a rigorous introduction to Support Vector Machines (SVMs) at the crossroads of geometry, convex optimization, and kernel methods. We review Euclidean geometry and Rosenblatt's perceptron, then develop the large-margin classifier: primal/dual formulations, KKT conditions, and the role of support vectors. Kernelization is formalized through RKHS and the representer theorem, enabling nonlinear decision boundaries. Extensions include soft-margin SVM, SVR, LS-SVM, multiclass strategies (OvR/OvO), and probability calibration (sigmoid, isotonic). The final part gathers practical modeling principles and hyperparameter tuning. The course targets Master's-level students with background in statistical learning, functional analysis, linear algebra, and optimization; technical sections and further readings are flagged throughout.

Suggested Citation

  • Yoann Pull, 2025. "Support Vector Machines," Post-Print hal-05331339, HAL.
    • Handle: RePEc:hal:journl:hal-05331339
    Note: View the original document on HAL open archive server: https://hal.science/hal-05331339v1
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    File URL: https://hal.science/hal-05331339v1/document
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    References listed on IDEAS

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    2. Yao, Xiao & Crook, Jonathan & Andreeva, Galina, 2015. "Support vector regression for loss given default modelling," European Journal of Operational Research, Elsevier, vol. 240(2), pages 528-538.
    3. Yao, Xiao & Crook, Jonathan & Andreeva, Galina, 2017. "Enhancing two-stage modelling methodology for loss given default with support vector machines," European Journal of Operational Research, Elsevier, vol. 263(2), pages 679-689.
    4. Loterman, Gert & Brown, Iain & Martens, David & Mues, Christophe & Baesens, Bart, 2012. "Benchmarking regression algorithms for loss given default modeling," International Journal of Forecasting, Elsevier, vol. 28(1), pages 161-170.
    5. Vladimir N. Vapnik, 1995. "The Nature of Statistical Learning Theory," Springer Books, Springer, number 978-1-4757-2440-0, August.
    6. Ellen Tobback & David Martens & Tony Van Gestel & Bart Baesens, 2014. "Forecasting Loss Given Default models: impact of account characteristics and the macroeconomic state," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(3), pages 376-392, March.
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