A. Blumer, A. Ehrenfeucht, D. Haussler and M. K. Warmuth, Learnability and the Vapnik-Chervonekis dimension, Journal of the ACM, 36 (1989) 929-965. Home/Search Document Not in Database Summary Related Articles Check |
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Structure Identification in Relational Data - Dechter, Pearl (1997) (61 citations) (Correct)
....every Horn theory that contains the latter must also contain the former. 2 Corollary 4.8 The V C dimension of (the class of) Horn theories is O[exp(n=2) Proof: The V C dimension is defined as the maximumnumber of points that can be shattered by Horn theories, in the sense of Corollary 4. 7 [5]. Accordingly, this number is equal to the maximumnumber of n tuples such that Independently proved in [28] 24 none is in the intersection closure of the rest, namely, n=2 ) O[exp(n=2) The V C dimension plays an important role in the framework of PAC learning, where it is used to ....
.... is in the intersection closure of the rest, namely, n=2 ) O[exp(n=2) The V C dimension plays an important role in the framework of PAC learning, where it is used to assess the number of random samples needed before the error associated with learning an incorrect theory can be bounded [5]. Roughly speaking, Corollary 4.8 states that approximately as many samples as the square root of the 2 possible tuples are needed before one can be fairly confident that the Horn theory learned does not deviate substantially from the one generating the data. Since the V C dimension grows ....
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A. Blumer, A. Ehrenfeucht, D. Haussler and M. K. Warmuth, Learnability and the Vapnik-Chervonekis dimension, Journal of the ACM, 36 (1989) 929-965.
Evaluation and Selection of Biases in Machine Learning - Gordon, Jardins (1995) (22 citations) (Correct)
....otherwise, it is incorrect. The computational learning community has also explored the issue of bias strength from a formal, analytical perspective. Vapnik and Chervonenkis [38] define a mea sure of the size of a bias defined by a given representation, called the VC dimension. Blumer et al. [7] use the VC dimension to provide bounds on the number of ex amples required for any consistent learning algorithm to approximate the target concept with high confidence. A pr ocedur al bias (also called algor ith,zic bias [26] determines the order of traver sal of the states in the space ....
Blumer, A., Ehreffeucht, A., Haussler, D., and Warmuth, M. (1989). Learnability and the Vapnik-Chervonekis dimension. Journal of the Association for Computing Machinery, 36(4):929 965.
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