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Primal and dual combinatorial dimensions

Kleer,Pieter
; 
Simon,Hans
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 classical 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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Publisher Copyright: © 2022 The Author(s)
Date
2023-03-15
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Tilburg University Research Output Collection
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Keywords
Dual dimension, Fat-shattering dimension, Pseudo-dimension, VC dimension
Citation
Kleer, P & Simon, H 2023, 'Primal and dual combinatorial dimensions', Discrete Applied Mathematics, vol. 327, pp. 185-196. https://doi.org/10.1016/j.dam.2022.11.010
URI
https://hdl.handle.net/20.500.14602/80151
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