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European Conference on Computational Learning Theory

EuroCOLT 1997: Computational Learning Theory pp 238–250Cite as

Linear Algebraic proofs of VC-Dimension based inequalities

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

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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References

  1. L.Babai and P.Frankl. Linear algebra methods in combinatorics with applications to geometry and computer science. (Preliminary Version 2), 1992, Dept. of Computer Science,The University of Chicago.

    Google Scholar 

  2. P.Frankl and R.M.Wilson. Intersection theorems with geometric consequences. Combinatorica 1(1981),357–368.

    Google Scholar 

  3. S.Floyd and M.Warmuth. Sample compression,learnability,and the Vapnik-Chervonenkis dimension, Machine Learning, 1–36, 1995.

    Google Scholar 

  4. E. Welzl.(1987). Complete range spaces.Unpublished notes.

    Google Scholar 

  5. D.Haussler and Phil Long.(1991) A generalization of Sauer's lemma, UCSC-CRL-90-15.

    Google Scholar 

  6. P.Goldberg and M.Jerrum (1993). Bounding the Vapnik-Chervonenkis dimension of concepts classes parameterized by real numbers. In proc. 6th Annual ACM Conference on Computational Learning Theory.

    Google Scholar 

  7. N.Sauer (1972). On the density of families of sets. J. Comb. Theory, Series A 13(1972), 145–147.

    Google Scholar 

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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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Editor information

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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