On the Additive Properties of the Fat-Shattering Dimension

被引：2

作者：

Asor, Ohad ^{[1
]}

Duan, Hubert Haoyang ^{[2
]}

Kontorovich, Aryeh ^{[3
]}

机构：

[1] Adv Comp Res & Dev, IL-76124 Rehovot, Israel

[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada

[3] Ben Gurion Univ Negev, Dept Comp Sci, IL-84105 Beer Sheva, Israel

来源：

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS | 2014年 / 25卷 / 12期

基金：

以色列科学基金会;

关键词：

Combinatorial dimension; fat-shattering; Minkowski addition; scale-sensitive; UNIFORM-CONVERGENCE;

D O I：

10.1109/TNNLS.2014.2327065

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

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.

引用

页码：2309 / 2312

页数：4

共 23 条

[1] Scale-sensitive dimensions, uniform convergence, and learnability [J].