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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Proceedings ArticleDOI
Predictive PAC Learnability: A Paradigm for Learning from Exchangeable Input Data
TL;DR: Using de Finetti's theorem, it is shown that if a universally separable function class $\mathscr F$ is distribution-free PAC learnable under i.i.d. inputs, then it is Distribution-free predictive PAC learnability under exchangeable inputs, with a slightly worse sample complexity.
Journal ArticleDOI
The degree of approximation of sets in Euclidean space using sets with bounded Vapnik-Chervonenkis dimension
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Proceedings ArticleDOI
Improved lower bounds for learning from noisy examples: an information-theoretic approach
TL;DR: This paper presents a general information-theoretic approach for obtaining lower bounds on the number of examples needed to PAC learn in the presence of noise, and the technique is applied to several different models, illustrating its generality and power.
References
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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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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.