• DocumentCode
    45000
  • Title

    On the Additive Properties of the Fat-Shattering Dimension

  • Author

    Asor, Ohad ; Duan, Hubert Haoyang ; Kontorovich, Aryeh

  • Author_Institution
    Adv. Comput. R&D, Rehovot, Israel
  • Volume
    25
  • Issue
    12
  • fYear
    2014
  • fDate
    Dec. 2014
  • Firstpage
    2309
  • Lastpage
    2312
  • Abstract
    The properties of the VC-dimension under various compositions are well-understood, but this is much less the case for classes of continuous functions. In this brief, we show that a commonly used scale-sensitive dimension, Vy, is much less well-behaved under Minkowski summation than its VC cousin, while the fat-shattering dimension retains some compositional similarity to the VC-dimension. As an application, we analyze the fat-shattering dimension of trigonometric functions and series.
  • Keywords
    learning (artificial intelligence); series (mathematics); Minkowski summation; VC-dimension; additive property; continuous functions; fat-shattering dimension; scale-sensitive dimension; trigonometric functions; trigonometric series; Additives; Boosting; Complexity theory; Convergence; Neural networks; Upper bound; Combinatorial dimension; Minkowski addition; fat-shattering; scale-sensitive; scale-sensitive.;
  • fLanguage
    English
  • Journal_Title
    Neural Networks and Learning Systems, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    2162-237X
  • Type

    jour

  • DOI
    10.1109/TNNLS.2014.2327065
  • Filename
    6828755
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=45000