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    We present a new bilevel cross-validation method for Support Vector Machine (SVM) model selection. This approach constructs the full regularization path using structured linear programs, improving model optimization.

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    Area of Science:

    • Machine Learning
    • Optimization Theory

    Background:

    • Support Vector Machines (SVMs) are widely used for classification.
    • Model selection in SVMs often involves complex hyperparameter tuning.
    • Existing methods may not efficiently explore the entire regularization path.

    Purpose of the Study:

    • To introduce a novel bilevel cross-validation scheme for SVM model selection.
    • To develop an efficient method for constructing the entire SVM regularization path.
    • To leverage nonsmooth optimization concepts for improved SVM training.

    Main Methods:

    • The proposed method constructs the entire regularization path of SVMs.
    • This path construction is framed as a particular case of proximal trajectories in nonsmooth optimization.
    • An algorithm based on solving a finite number of structured linear programs is employed.
    • The methodology operates directly on the primal form of SVM.

    Main Results:

    • The bilevel cross-validation scheme enables comprehensive model selection.
    • The algorithm efficiently generates the SVM regularization path.
    • Numerical results demonstrate the effectiveness on binary datasets.

    Conclusions:

    • The proposed bilevel cross-validation scheme offers an effective approach for SVM model selection.
    • The method's reliance on structured linear programs provides computational advantages.
    • This work contributes to the advancement of SVM optimization techniques.