Journal ArticleDOI
Learnability and the Vapnik-Chervonenkis dimension
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
Citations
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Journal ArticleDOI
Bayesian applications of belief networks and multilayer perceptrons for ovarian tumor classification with rejection
TL;DR: A hybrid Bayesian methodology that consists in encoding prior knowledge in the form of a (Bayesian) belief network and then using this knowledge to estimate an informative prior for a black-box model (e.g. a multilayer perceptron) is proposed.
Proceedings ArticleDOI
Learning with a slowly changing distribution
TL;DR: An upper bound on &Ugr; is given that ensures learning is possible from a finite number of examples, to ensure that some learning algorithm can produce an acceptably small probability of misclassification.
Journal ArticleDOI
Can PAC learning algorithms tolerate random attribute noise
Sally A. Goldman,Robert H. Sloan +1 more
TL;DR: It is shown that product random attribute noise, where each attributei is flipped randomly and independently with its own probability pi, is nearly as harmful as malicious noise-no algorithm can tolerate more than a very small amount of such noise.
Journal ArticleDOI
Lower bounds in pattern recognition and learning
Luc Devroye,Gábor Lugosi +1 more
TL;DR: Lower bounds are derived for the performance of any pattern recognition algorithm, which, using training data, selects a discrimination rule from a certain class of rules, and the bounds involve the Vapnik-Chervonenkis dimension of the class and the minimal error probability within the class.
Proceedings ArticleDOI
General bounds on the number of examples needed for learning probabilistic concepts
TL;DR: A new method for designing learning algorithms: dynamic partitioning of the domain by use of splitting trees is introduced and it can be shown that the resulting lower bounds for learning ND are tight to within a logarithmic factor.
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.
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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.
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Pattern Classification and Scene Analysis.
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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.