Learnability and the Vapnik-Chervonenkis dimension
Citations
27 citations
Cites background from "Learnability and the Vapnik-Chervon..."
...We consider the usual two-phase process of decision tree learning; after growing a tree, it is pruned in order to reduce its dependency on thegrowing data and to better reflect characteristics of future data....
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27 citations
Cites background from "Learnability and the Vapnik-Chervon..."
...It is well known that there are poly(n)-time PAC learning algorithms for the concept class of linear threshold functions over {0, 1}n; this follows from information-theoretic sample complexity arguments [8, 9] combined with the existence of polynomial-time algorithms for linear programming [23]....
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...There are well-known polynomial-time PAC learning algorithms for concept classes consisting of simple functions such as conjunctions and disjunctions [39], decision lists [35], parity functions [15, 18], and halfspaces [9]....
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27 citations
27 citations
Cites background from "Learnability and the Vapnik-Chervon..."
...The number of examples needed for valid learning in standard probabilistic models of learning can be quantified fairly precisely by the VC-dimension of the class of functions being used as hypotheses (that is, as the functions chosen to approximate to the training data); see [2, 8], for example ....
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...TheVapnik-Chervonenkis dimension [46, 8] of H is defined as the maximum (possibly infinite, in the case where the domain is R) such thatΠH(m) = 2....
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27 citations
Cites background from "Learnability and the Vapnik-Chervon..."
...In the past, researchers have concentrated on the "learnability" of concept classes whose sample spaces are, of course (otherwise the problem would be trivial), superpolynomial [31], [4], [25], [12], although efficient sampling was studied, for example, in [1 I]....
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...More discussion and justification of this model can be found in [4], [16], [18], and [32]....
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References
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