Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic Upper Bound for Recursive Teaching Dimension of Finite VC
  Classes   In this work we study the quantitative relation between the recursive
teaching dimension (RTD) and the VC dimension (VCD) of concept classes of
finite sizes. The RTD of a concept class $\mathcal C \subseteq \{0, 1\}^n$,
introduced by Zilles et al. (2011), is a combinatorial complexity measure
characterized by the worst-case number of examples necessary to identify a
concept in $\mathcal C$ according to the recursive teaching model.
  For any finite concept class $\mathcal C \subseteq \{0,1\}^n$ with
$\mathrm{VCD}(\mathcal C)=d$, Simon & Zilles (2015) posed an open problem
$\mathrm{RTD}(\mathcal C) = O(d)$, i.e., is RTD linearly upper bounded by VCD?
Previously, the best known result is an exponential upper bound
$\mathrm{RTD}(\mathcal C) = O(d \cdot 2^d)$, due to Chen et al. (2016). In this
paper, we show a quadratic upper bound: $\mathrm{RTD}(\mathcal C) = O(d^2)$,
much closer to an answer to the open problem. We also discuss the challenges in
fully solving the problem.

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The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: eess