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
Citations
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Proceedings ArticleDOI
On the sample complexity of weak learning
TL;DR: The sample complexity of weak learning was studied in this paper, where it was shown that the distribution-free sample size required to obtain a small advantage in prediction over random guessing is essentially equal to that required to achieve arbitrary accuracy.
Posted Content
VC dimension of ellipsoids
Yohji Akama,Kei Irie +1 more
TL;DR: It is established that the VC dimension of the class of d-dimensional ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component d- dimensional Gaussian mixture models induces a geometric class having VC dimension at least N(d^ 2+3D)/2.
Journal ArticleDOI
Robust cutpoints in the logical analysis of numerical data
Martin Anthony,Joel Ratsaby +1 more
TL;DR: This paper analyzes the predictive performance of logical analysis of binary data techniques and derives generalization error bounds that depend on how 'robust' the cutpoints are.
Journal ArticleDOI
N-learners problem: fusion of concepts
TL;DR: By using a linear threshold fusion function (of the outputs of individual learners) it is shown that the composite system can be made better than the best of the statistically independent learners.
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.
Journal ArticleDOI
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.