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
Learning by canonical smooth estimation. II. Learning and choice of model complexity
K.L. Buescher,P.R. Kumar +1 more
TL;DR: This paper analyzes the properties of a procedure for learning from examples based on a canonical error estimator developed in Part I, and shows that for a broad class of learning problems, the set of cases for which such empirical error minimization works is a proper subset of the Cases for which the canonical learner works.
Journal ArticleDOI
Vapnik-Chervonenkis bounds for generalization
TL;DR: In this paper, the authors review the Vapnik and Chervonenkis theorem as applied to the problem of generalization and derive tighter bounds and a new version of the theorem bounding the accuracy in the estimation of the generalization probabilities from finite samples.
Journal ArticleDOI
The VC dimension of k-fold union
David Eisenstat,Dana Angluin +1 more
TL;DR: The known O(dklogk) bound on the VC dimension of k-fold unions or intersections of a given concept class with VC dimension d is shown to be asymptotically tight.
Book ChapterDOI
Using the Pseudo-Dimension to Analyze Approximation Algorithms for Integer Programming
TL;DR: Approximation guarantees for randomized algorithms for packing and covering integer programs expressed in certain normal forms are proved and applications are described to a generalization of Dominating Set motivated by distributed file sharing applications, to an optimization problem motivated by an analysis of boosting, and to ageneralization of matching in hypergraphs.
Journal ArticleDOI
A connectionist learning algorithm with provable generalization and scaling bounds
TL;DR: A connectionist learning algorithm, the bounded, randomized, distributed (BRD) algorithm, is presented and formally analyzed within the framework of computational learning theory, and a new class of connectionist concepts is shown to be polynomially learnable using the BRD algorithm.
References
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Book
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.