Results on learnability and the Vapnik-Chervonenkis dimension
نویسندگان
چکیده
منابع مشابه
Results on Learnability and the Vapnik-Chervonenkis Dimension*
We consider the problem of learning a concept from examples in the distributionfree model by Valiant. (An essentially equivalent model, if one ignores issues of computational difficulty, was studied by Vapnik and Chervonenkis.) We introduce the notion of dynamic sampling, wherein the number of examples examined may increase with the complexity of the target concept. This method is used to estab...
متن کاملResults on learnability and the Vapnik-Chervonenkis dimension (Extended Abstract)
We consider the problem of learning a concept from examples in the distributionfree model by Valiant. (An essentially equivalent model, if one ignores issues of computational difficulty, was studied by Vapnik and Chervonenkis.) We introduce the notion of dynamic sampling, wherein the number of examples examined may increase with the complexity of the target concept. This method is used to estab...
متن کاملVapnik-chervonenkis Dimension 1 Vapnik-chervonenkis Dimension
Valiant’s theorem from the previous lecture is meaningless for infinite hypothesis classes, or even classes with more than exponential size. In 1968, Vladimir Vapnik and Alexey Chervonenkis wrote a very original and influential paper (in Russian) [5, 6] which allows us to estimate the sample complexity for infinite hypothesis classes too. The idea is that the size of the hypothesis class is a p...
متن کاملVapnik-Chervonenkis Dimension and (Pseudo-)Hyperplane Arrangements
An arrangement of oriented pseudohyperplanes in affine d-space defines on its set X of pseudohyperplanes a set system (or range space) (X,R), R ⊆ 2 of VCdimension d in a natural way: to every cell c in the arrangement assign the subset of pseudohyperplanes having c on their positive side, and let R be the collection of all these subsets. We investigate and characterize the range spaces correspo...
متن کاملOn the Vapnik–Chervonenkis dimension of the Ising perceptron
The Vapnik–Chervonenkis (VC) dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes N 6 31. It is significantly larger than 1 2N . The data suggest that there is probably no well-defined asymptotic behaviour for N → ∞. The Vapnik–Chervonenkis (VC) dimension is one of the central quantities used in both mathematical statistics and computer...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 1991
ISSN: 0890-5401
DOI: 10.1016/0890-5401(91)90058-a