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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Journal ArticleDOI
Statistical mechanics calculation of Vapnik-Chervonenkis bounds for perceptrons
Andreas Engel,Wolfgang Fink +1 more
TL;DR: This work considers both spherical and Ising constraints on the couplings of the perceptron, investigates learnable as well as unlearnable problems and study the special situation where the class of perceptrons considered is restricted to the version space.
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EPTAS for Max Clique on Disks and Unit Balls
TL;DR: A polynomial-time algorithm is proposed which takes as input a finite set of points of R^3 and computes, up to arbitrary precision, a maximum subset with diameter at most 1, and gives the first randomized EPTAS and deterministic PTAS for Maximum Clique in unit ball graphs.
Journal ArticleDOI
A Theoretical and Empirical Study of a Noise-TolerantAlgorithm to Learn Geometric Patterns
TL;DR: An efficient noise-tolerant algorithm (designed using the statistical query model) to learn the class of one-dimensional geometric patterns and an empirical study of the algorithm provides some evidence that statistical query algorithms may be valuable for use in practice for handling noisy data.
Book ChapterDOI
Learning Boolean functions with genetic algorithms: a PAC analysis
TL;DR: A class of genetic algorithms for learning Boolean conjuncts and disjuncts is presented and analyzed in the context of the distribution-free learnability model and the main result provides the number of generations and the size of the population sufficient for the GA to accomplish the learning task.
Book ChapterDOI
Sharpening Occam's Razor
TL;DR: A new representation-independent formulation of Occam's razor theorem, based on Kolmogorov complexity, is provided, which achieves a sharper reverse of Occams razor theorem than that of [5], and extends the reverse to superpolynomial running times.
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.
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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.
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.