Learnability and the Vapnik-Chervonenkis dimension
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"Learnability and the Vapnik-Chervon..." refers background or methods in this paper
...For the “only if” part, note first that by Theorem 2.l(ii)(b), any learning algorithm for C must use a sample size that grows linearly in the VC dimension of C,,, and hence if the VC dimension of C, is not polynomial in ~1, then C is not poly-learnable by any hypothesis space H. To show that C being poly-learnable implies that there is an r-poly hy-fi for C, we use a construction from [ 52 ]....
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...The above example shows that it is not only useful to parameterize learning algorithms and learnability results by the dimension of the domain, but also by some natural measure of the syntactic complexity of the target concept, in this case the number of intervals used to define it. Both of these considerations are emphasized in [36] and [ 52 ] in the investigation into the learnability of Boolean functions....
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...The functional and oracle models of polynomial learnability are shown to be equivalent in [30], along with another variant of the oracle model in which there are two probability distributions on the domain X, and two oracles, one for positive examples of the target concept and one for negative examples (e.g., [36] and [ 52 ])....
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...It is also possible to allow the computation time to depend explicitly on the accuracy and confidence parameters t and 6. Since this, and other extensions of the above model, are allowed in the definition of polynomial learnability in [ 52 ] and [59], we now introduce a second model of polynomial learnability, which we call the oracle model (see also [3] and [36])....
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...These notions of polynomial learnability, both closely related to the model introduced in [59] and elaborated in [36] and [ 52 ], are discussed in Sections 3.1 and 3.2, respectively....
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"Learnability and the Vapnik-Chervon..." refers methods in this paper
...The techniques we have described in this paper are easily applied to these domains, and generally give better results than the simple counting argument of Theorem 2.2 [ 28 ]....
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