Learnability and the Vapnik-Chervonenkis dimension
Citations
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Cites background from "Learnability and the Vapnik-Chervon..."
...In this case, it is well known that the learnability of ' is completely characterized by the finiteness of a simple combinatorial quantity known as the Vapnik Chervonenkis (VC) dimension of ' [Vapnik and Chervonenkis 1971; Blumer et al. 1989]....
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...In this case it is well known that the learnability of H is completely characterized by the finiteness of a simple combinatorial quantity known as the Vapnik-Chervonenkis (VC) dimension of H [24, 6]....
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396 citations
Cites background from "Learnability and the Vapnik-Chervon..."
...Theorem 4 (Blumer et al. 1989)....
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...The following well-known theorem (see Kearns & Vazirani (1994) or Blumer et al. (1989)) gives a bound on the size of the sample so that a hypothesis that is consistent with the sample also has, with high probability, small error with respect to the entire distribution....
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...The theorem below is a slight variant of a similar theorem from Blumer et al. (1989)....
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380 citations
Cites methods from "Learnability and the Vapnik-Chervon..."
...Although we omit the details, these arguments can be made rigorous using, for instance, the randomized lower bound techniques of Blumer et al. (1989) ....
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...It follows from standard arguments ( Blumer, Ehrenfeucht, Haussler & Warmuth, 1989 ) that if the Vapnik-Chervonenkis dimension of T is polynomially bounded by the complexity parameter n, an algorithm that efficiently solves the disagreement minimization problem for T can be used as a subroutine by an efficient algorithm for learning fir" in the agnostic PAC model....
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References
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