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Adaptive L0 Regularization for Sparse Support Vector Regression

Author

Listed:
  • Antonis Christou

    (School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK)

  • Andreas Artemiou

    (School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK)

Abstract

In this work, we proposed a sparse version of the Support Vector Regression (SVR) algorithm that uses regularization to achieve sparsity in function estimation. To achieve this, we used an adaptive L 0 penalty that has a ridge structure and, therefore, does not introduce additional computational complexity to the algorithm. In addition to this, we used an alternative approach based on a similar proposal in the Support Vector Machine (SVM) literature. Through numerical studies, we demonstrated the effectiveness of our proposals. We believe that this is the first time someone discussed a sparse version of Support Vector Regression (in terms of variable selection and not in terms of support vector selection).

Suggested Citation

  • Antonis Christou & Andreas Artemiou, 2023. "Adaptive L0 Regularization for Sparse Support Vector Regression," Mathematics, MDPI, vol. 11(13), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2808-:d:1176868
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    References listed on IDEAS

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    1. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    2. Florian Frommlet & Grégory Nuel, 2016. "An Adaptive Ridge Procedure for L0 Regularization," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-23, February.
    3. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    4. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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