# 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 language English 2327065 2309-2312 4 IEEE Transactions on Neural Networks and Learning Systems 25 12 https://doi.org/10.1109/TNNLS.2014.2327065 Published - 1 Dec 2014

## Keywords

• Combinatorial dimension