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
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Book ChapterDOI
Quantifying the amount of verboseness (extended abstract)
TL;DR: A complete characterization is obtained relating the question to finite combinatorics of the classification of sets of natural numbers A according to the number of queries which are needed to compute the n-fold characteristic function of A.
Proceedings ArticleDOI
Unlabeled Data Does Provably Help
TL;DR: It is shown that the "label-complexity gap"' between the semi-supervised and the fully supervised setting can become arbitrarily large for concept classes of infinite VC-dimension (or sequences of classes whose VC-dimensions are finite but become arbitrary large).
Proceedings ArticleDOI
Sample sizes for sigmoidal neural networks
TL;DR: The theory of Probably Approximately Correct (PAC) learning is applied to feedforward neural networks with sigmoidal activation functions and it is shown that the asymptotic bound on the sample size required for learning with increasing accuracy 1 – c and decreasing probabllty of failure d is o((l/e)(wlog(l/c) + (WN)2 +log( l/6)),
Book ChapterDOI
Applying valiant's learning framework to Al concept-learning problems
TL;DR: An overview of some recent theoretical results in the learning framework introduced by Valiant and further developed and a comparison to the work of Mitchell on version spaces are presented.
Journal ArticleDOI
Improving the Generalization Capacity of Cascade Classifiers
TL;DR: This work aims at improving the generalization capacity of the cascade classifier by controlling its complexity, which depends on the model of their classifier stages, the number of stages, and the feature space dimension of each stage, which can be controlled by integrating the parameter setting of the feature extractor into the maximum-margin framework of support vector machine training.
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.