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A Labelled Sample Compression Scheme of Size at Most Quadratic in the VC Dimension

Farnam MansouriSandra Zilles
Dec 2022
摘要
This paper presents a construction of a proper and stable labelled samplecompression scheme of size $O(\VCD^2)$ for any finite concept class, where$\VCD$ denotes the Vapnik-Chervonenkis Dimension. The construction is based ona well-known model of machine teaching, referred to as recursive teachingdimension. This substantially improves on the currently best known bound on thesize of sample compression schemes (due to Moran and Yehudayoff), which isexponential in $\VCD$. The long-standing open question whether the smallestsize of a sample compression scheme is in $O(\VCD)$ remains unresolved, but ourresults show that research on machine teaching is a promising avenue for thestudy of this open problem. As further evidence of the strong connections between machine teaching andsample compression, we prove that the model of no-clash teaching, introduced byKirkpatrick et al., can be used to define a non-trivial lower bound on the sizeof stable sample compression schemes.
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