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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Interactive Proofs for Verifying Machine Learning.
TL;DR: It is proved that for a specific hypothesis class, verification is significantly cheaper than learning in terms of sample complexity, even if the verifier engages with the prover only in a single-round (NP-like) protocol, and that verification is not always more efficient.
Journal ArticleDOI
Maximizing agreements and coagnostic learning
Nader H. Bshouty,Lynn Burroughs +1 more
TL;DR: This paper studies ?
Book ChapterDOI
Recent Advances in Decision Bireducts: Complexity, Heuristics and Streams
TL;DR: Some new results related to NP-hardness of extraction of optimal decision bireducts are reported, including heuristics aimed at searching for sub-optimal decision biresucts, and applications of decision bireucts to stream data mining.
Journal ArticleDOI
The complexity of theory revision
TL;DR: In this paper, the authors provide sample and computational complexity bounds for the problem of theory revision, and show that unless P = NP, no polynomial-time algorithm can identify this optimal revision, even given the exact distribution of queries, except in certain simple situations.
Journal ArticleDOI
Learning by Distances
TL;DR: A model of learning by distances is presented and Insight gained is applied to show that every class of subsets C that has a finite VC-dimension is PAC-learnable with respect to any fixed distribution.
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.