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Linear Algebraic proofs of VC-Dimension based inequalities

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Computational Learning Theory (EuroCOLT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1208))

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Abstract

We apply linear algebra(polynomial) techniques to various VC-Dimension based inequalities. We explore connections between the sample compression and this technique for so called maximum classes and prove that maximum classes are connected subgraphs of a Boolean cube.We provide a fast (linear in the cardinality of the class for the fixed VC-dimension) interpolational algorithm for maximum classes.A new method to bound a pseudo-dimension for a class of cell-wise constant functions is proposed.

Research at Rutgers partially supported by the US Air Force Grant AFOSR-94-0293.

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Author information

Authors and Affiliations

  1. NEC Research Institute, 4 Independence Way, 08540, Princeton, NJ

    Leonid Gurvits

  2. DIMACS, Rutgers University, 08903, New Brunswick, NJ

    Leonid Gurvits

Authors
  1. Leonid Gurvits
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Shai Ben-David

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© 1997 Springer-Verlag Berlin Heidelberg

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Gurvits, L. (1997). Linear Algebraic proofs of VC-Dimension based inequalities. In: Ben-David, S. (eds) Computational Learning Theory. EuroCOLT 1997. Lecture Notes in Computer Science, vol 1208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62685-9_20

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  • DOI: https://doi.org/10.1007/3-540-62685-9_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62685-5

  • Online ISBN: 978-3-540-68431-2

  • eBook Packages: Springer Book Archive

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