Learnability and the Vapnik-Chervonenkis dimension
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1,052 citations
Cites background from "Learnability and the Vapnik-Chervon..."
...The study draws an analogy between the role of the VC dimension (Blumer et al. (1989)) and the size of the family of hypothesis spaces |{H}|....
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1,037 citations
Cites background or methods from "Learnability and the Vapnik-Chervon..."
..., 2005) or the size of the smallest ǫ-cover (Benedek and Itai, 1991), rather than VC dimension (Blumer et al., 1989; Kearns and Vazirani, 1994)....
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...In particular, in the PAC model there is purposefully a complete disconnect between the data distribution D and the target function f being learned (Valiant, 1984; Blumer et al., 1989; Kearns and Vazirani, 1994)....
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1,027 citations
Cites background from "Learnability and the Vapnik-Chervon..."
...On the other hand, the VC-dimension of gn is 2n-1 (since the set {0y : y E {0, 1}n-1}is shattered by gn)....
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...…1 -o/2 over the additional sample, f is rejected. e In particular, the above proposition implies that if for every n, gn has polynomial (in n) VC-dimension [Vapnik and Chervonenkis 1971; Blumer et al. 1989],12 then g has a tester whose sample complexity is polynomial in n,1/E, and log(1/o)....
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...Every class that is learnable with constant confidence using a sample of size poly(n/e) (and thus has a poly(n) VC dimension [Blumer et al. 1989]), is testable with a poly(n/e) z log(1/d) sample (in at most exponential time)....
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...In particular, the above proposition implies that if for every n, ^n has polynomial (in n) VC-dimension [Vapnik and Chervonenkis 1971; Blumer et al. 1989],(12) then ^ has a tester whose sample complexity is polynomial in n, 1/e, and log(1/d)....
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...By Blumer et al. [1989], learning this class requires a sample of size i(2n). e The impossibility of learning the function class in Proposition 3.3.1 is due to its exponential VC-dimension, (i.e., it is a pure information theoretic consideration)....
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References
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