原始和对偶组合维数
Primal and Dual Combinatorial Dimensions
摘要：
本文给出了多值函数类的伪维数、脂肪分解维数等组合维数的原维数与对偶维数之间关系的严格界。这些维度的概念在学习理论领域起着重要的作用。我们首先回顾了一些（民间传说）的结果，约束的对偶维数的函数类，其原始的，并在此之后，给（几乎）匹配的下界。特别是，我们给出了一个适当的推广，以多值函数类的一个众所周知的界限，由于Assouad（1983），它涉及到一个二元函数类的原始和对偶VC-维。
英文摘要：
We give tight bounds on the relation between the primal and dual of various combinatorial dimensions, such as the pseudo-dimension and fat-shattering dimension, for multi-valued function classes. These dimensional notions play an important role in the area of learning theory. We first review some (folklore) results that bound the dual dimension of a function class in terms of its primal, and after that give (almost) matching lower bounds. In particular, we give an appropriate generalization to multi-valued function classes of a well-known bound due to Assouad (1983), that relates the primal and dual VC-dimension of a binary function class.
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