Journal ArticleDOI
Learnability and the Vapnik-Chervonenkis dimension
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TLDR
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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Teachability in computational learning
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TL;DR: A notion of teachability is introduced with which to establish a relationship between the learnability and teachability and the complexity issues of a teacher in relation to learning are discussed.
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Theory and applications of agnostic PAC-learning with small decision trees
TL;DR: The performance of this theoretically founded algorithm T2, an agnostic PAC-learning of decision trees of at most 2 levels, is evaluated on 15 common “real-world” datasets, and it is shown that for most of these datasets T2 provides simple decision trees with little or no loss in predictive power.
Proceedings ArticleDOI
How to net a lot with little: small ε-nets for disks and halfspaces
TL;DR: In this paper, it was shown that disks and pseudo-disks in the plane as well as halfspaces in R3 allow e-nets of size only O(1/e), which is best possible up to a multiplicative constant.
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On the difficulty of approximately maximizing agreements
TL;DR: In this article, it was shown that unless P = NP, there is no polynomial time approximation scheme for finding a member in the class that approximately maximizes the agreement with a given training sample.
References
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Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Journal ArticleDOI
Pattern Classification and Scene Analysis.
Book
Pattern classification and scene analysis
Richard O. Duda,Peter E. Hart +1 more
TL;DR: In this article, a unified, comprehensive and up-to-date treatment of both statistical and descriptive methods for pattern recognition is provided, including Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis, clustering, preprosessing of pictorial data, spatial filtering, shape description techniques, perspective transformations, projective invariants, linguistic procedures, and artificial intelligence techniques for scene analysis.