Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primal and Dual Combinatorial Dimensions   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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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an