Support Vector Machines

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

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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.

Keywords: Support Vector Machines (SVM); Convex optimization; Kernel methods; Optimisation convexe (search for similar items in EconPapers)
Date: 2025-10-13
Note: View the original document on HAL open archive server: https://hal.science/hal-05331339v1
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Published in Master. Support Vector Machines, France. 2025, pp.30

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