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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Book ChapterDOI
Logical Minimisation of Meta-Rules Within Meta-Interpretive Learning
Andrew Cropper,Stephen Muggleton +1 more
TL;DR: This paper demonstrates that irreducible, or minimal sets of meta-rules can be found automatically by applying Plotkin's clausal theory reduction algorithm and shows that in some cases as few as two meta- rules are complete and sufficient for generating all hypotheses.
Proceedings ArticleDOI
Synthesis of optimal switching logic for hybrid systems
TL;DR: This paper generalizes earlier work on synthesis for safety by presenting an approach for specifying quantitative measures using reward and penalty functions, and illustrating its effectiveness using several examples.
Proceedings ArticleDOI
Learning with unreliable boundary queries
TL;DR: A model for learning from examples and membership queries in situations where the boundary between positive and negative examples is somewhat ill-defined is introduced, and an algorithm that learns the intersection of two halfspaces whose bounding planes pass through the origin in the PAC-with-membership-queries model is extended.
Book ChapterDOI
Approximate Testing of Visual Properties
TL;DR: This work studies visual properties of discretized images represented by n× n matrices of binary pixel values and obtains algorithms with query complexity independent of n for several basic properties: being a half-plane, connectedness and convexity.
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.