On the Additive Properties of the Fat-Shattering Dimension Academic Article uri icon


  • 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 y, 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.

publication date

  • January 1, 2014