Item request has been placed! ×
Item request cannot be made. ×
loading  Processing Request

Theoretical aspects of robust SVM optimization in Banach spaces and Nash equilibrium interpretation

Item request has been placed! ×
Item request cannot be made. ×
loading   Processing Request
  • معلومة اضافية
    • Contributors:
      Ecole Nationale de l'Aviation Civile (ENAC); Institut de Mathématiques de Toulouse UMR5219 (IMT); Université Toulouse Capitole (UT Capitole); Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse); Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J); Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3); Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS); ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019)
    • بيانات النشر:
      HAL CCSD
      Springer Verlag
    • الموضوع:
      2024
    • Collection:
      Université Toulouse 2 - Jean Jaurès: HAL
    • نبذة مختصرة :
      International audience ; There are many real life applications where data can not be effectively represented in Hilbert spaces and/or where the data points are uncertain. In this context, we address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalized to their robust counterpart in Banach spaces. These include the representer theorem, strong duality for the associated optimization problem as well as their geometrical interpretation. Furthermore, we propose a game theoretical interpretation of the class separation problem when the underlying space is reflexive and smooth. The proposed Nash equilibrium formulation draws connections and emphasizes the interplay between class separation in machine learning and game theory in the general setting of Banach spaces.
    • Relation:
      hal-04447192; https://enac.hal.science/hal-04447192; https://enac.hal.science/hal-04447192/document; https://enac.hal.science/hal-04447192/file/Robust_SVM_Banach_pln.pdf
    • الرقم المعرف:
      10.1007/s10472-024-09931-z
    • الدخول الالكتروني :
      https://enac.hal.science/hal-04447192
      https://enac.hal.science/hal-04447192/document
      https://enac.hal.science/hal-04447192/file/Robust_SVM_Banach_pln.pdf
      https://doi.org/10.1007/s10472-024-09931-z
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.39FEED24