title: On the additive properties of the fat-shattering dimension.
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, Vγ, 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.
authors.forename: Ohad
authors.initials: O
authors.lastname: Asor
authors.forename: Hubert Haoyang
authors.initials: HH
authors.lastname: Duan
authors.forename: Aryeh
authors.initials: A
authors.lastname: Kontorovich