Primal and Dual Combinatorial Dimensions
Combinatorics
2021-08-24 v1 Discrete Mathematics
Machine Learning
Abstract
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.
Cite
@article{arxiv.2108.10037,
title = {Primal and Dual Combinatorial Dimensions},
author = {Pieter Kleer and Hans Simon},
journal= {arXiv preprint arXiv:2108.10037},
year = {2021}
}