On the additive properties of the fat-shattering dimension

Ohad Asor, Hubert Haoyang Duan, Aryeh Kontorovich

Research output: Contribution to journalArticlepeer-review

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, \(V-\gamma \) , 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.

Original languageEnglish
Article number2327065
Pages (from-to)2309-2312
Number of pages4
JournalIEEE Transactions on Neural Networks and Learning Systems
Volume25
Issue number12
DOIs
StatePublished - 1 Dec 2014

Keywords

  • Combinatorial dimension
  • Minkowski addition
  • fat-shattering
  • scale-sensitive.

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