IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v222y2014i1p197-21110.1007-s10479-012-1304-1.html
   My bibliography  Save this article

Regression tasks in machine learning via Fenchel duality

Author

Listed:
  • Radu Boţ
  • André Heinrich

Abstract

Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach for regression is investigated under a theoretical point of view that makes use of convex analysis and Fenchel duality. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the optimal solutions of the dual problem. Corresponding dual problems are then derived for different loss functions. The theoretical results are applied by numerically solving the regression task for two data sets and the accuracy of the regression when choosing different loss functions is investigated. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Radu Boţ & André Heinrich, 2014. "Regression tasks in machine learning via Fenchel duality," Annals of Operations Research, Springer, vol. 222(1), pages 197-211, November.
    • Handle: RePEc:spr:annopr:v:222:y:2014:i:1:p:197-211:10.1007/s10479-012-1304-1
    DOI: 10.1007/s10479-012-1304-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1304-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-012-1304-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bot, Radu Ioan & Lorenz, Nicole, 2011. "Optimization problems in statistical learning: Duality and optimality conditions," European Journal of Operational Research, Elsevier, vol. 213(2), pages 395-404, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. S. K. Mishra & Vinay Singh & Vivek Laha, 2016. "On duality for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 243(1), pages 249-272, August.
    2. Qingjie Hu & Jiguang Wang & Yu Chen, 2020. "New dualities for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 287(1), pages 233-255, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brandner, Hubertus & Lessmann, Stefan & Voß, Stefan, 2013. "A memetic approach to construct transductive discrete support vector machines," European Journal of Operational Research, Elsevier, vol. 230(3), pages 581-595.
    2. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.
    3. Corne, David & Dhaenens, Clarisse & Jourdan, Laetitia, 2012. "Synergies between operations research and data mining: The emerging use of multi-objective approaches," European Journal of Operational Research, Elsevier, vol. 221(3), pages 469-479.
    4. Radu Boţ & Christopher Hendrich, 2015. "A variable smoothing algorithm for solving convex optimization problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 124-150, April.
    5. Toriello, Alejandro & Vielma, Juan Pablo, 2012. "Fitting piecewise linear continuous functions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 86-95.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:222:y:2014:i:1:p:197-211:10.1007/s10479-012-1304-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.