Journal ArticleDOI
Learnability and the Vapnik-Chervonenkis dimension
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This paper shows that the essential condition for distribution-free learnability is finiteness of the Vapnik-Chervonenkis dimension, a simple combinatorial parameter of the class of concepts to be learned.Abstract:
Valiant's learnability model is extended to learning classes of concepts defined by regions in Euclidean space En. The methods in this paper lead to a unified treatment of some of Valiant's results, along with previous results on distribution-free convergence of certain pattern recognition algorithms. It is shown that the essential condition for distribution-free learnability is finiteness of the Vapnik-Chervonenkis dimension, a simple combinatorial parameter of the class of concepts to be learned. Using this parameter, the complexity and closure properties of learnable classes are analyzed, and the necessary and sufficient conditions are provided for feasible learnability.read more
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References
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Journal ArticleDOI
Occam's razor
TL;DR: It is shown that a polynomial learning algorithm, as defined by Valiant (1984), is obtained whenever there exists aPolynomial-time method of producing, for any sequence of observations, a nearly minimum hypothesis that is consistent with these observations.
Journal ArticleDOI
Learning Decision Lists
TL;DR: This paper introduces a new representation for Boolean functions, called decision lists, and shows that they are efficiently learnable from examples, and strictly increases the set of functions known to be polynomially learnable, in the sense of Valiant (1984).
Journal ArticleDOI
Learning From Noisy Examples
Dana Angluin,Philip Laird +1 more
TL;DR: This paper shows that when the teacher may make independent random errors in classifying the example data, the strategy of selecting the most consistent rule for the sample is sufficient, and usually requires a feasibly small number of examples, provided noise affects less than half the examples on average.
Journal ArticleDOI
ź-nets and simplex range queries
David Haussler,Emo Welzl +1 more
TL;DR: The concept of an ɛ-net of a set of points for an abstract set of ranges is introduced and sufficient conditions that a random sample is an Â-net with any desired probability are given.