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Sélection de modèle par chemin de régularisation pour les machines à vecteurs support à coût quadratique

Rémi Bonidal 1 
1 ABC - Machine Learning and Computational Biology
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : Model selection is of major interest in statistical learning. In this document, we introduce model selection methods for bi-class and multi-class support vector machines. We focus on quadratic loss machines, i.e., machines for which the empirical term of the objective function of the learning problem is a quadratic form. For SVMs, model selection consists in finding the optimal value of the regularization coefficient and choosing an appropriate kernel (or the values of its parameters). The proposed methods use path-following techniques in combination with new model selection criteria. This document is structured around three main contributions. The first one is a method performing model selection through the use of the regularization path for the l2-SVM. In this framework, we introduce new approximations of the generalization error. The second main contribution is the extension of the first one to the multi-category setting, more precisely the M-SVM². This study led us to derive a new M-SVM, the least squares M-SVM. Additionally, we present new model selection criteria for the M-SVM introduced by Lee, Lin and Wahba (and thus the M-SVM²). The third main contribution deals with the optimization of the values of the kernel parameters. Our method makes use of the principle of kernel-target alignment with centered kernels. It extends it through the introduction of a regularization term. Experimental validation of these methods was performed on classical benchmark data, toy data and real-world data
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Submitted on : Thursday, March 29, 2018 - 12:28:11 PM
Last modification on : Saturday, October 16, 2021 - 11:26:08 AM
Long-term archiving on: : Friday, September 14, 2018 - 10:34:28 AM


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  • HAL Id : tel-01264027, version 2


Rémi Bonidal. Sélection de modèle par chemin de régularisation pour les machines à vecteurs support à coût quadratique. Apprentissage [cs.LG]. Université de Lorraine, 2013. Français. ⟨NNT : 2013LORR0066⟩. ⟨tel-01264027v2⟩



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