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
Citations
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Proceedings ArticleDOI
Bias-variance tradeoffs in program analysis
TL;DR: It is shown that bias-variance tradeoffs, an idea from learning theory, can be used to explain why more precise abstractions do not necessarily lead to better results and also provides practical techniques for coping with such limitations.
Journal ArticleDOI
On the hardness of learning intersections of two halfspaces
Subhash Khot,Rishi Saket +1 more
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Min-max classifiers: Learnability, design and application☆
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TL;DR: Several subclasses of thresholded min-max functions are shown to be learnable, generalizing the learnability results for the corresponding classes of Boolean functions.
Book ChapterDOI
Estimating the Optimal Margins of Embeddings in Euclidean Half Spaces
TL;DR: The singular value decomposition of this matrix is used to determine the optimal margins of embeddings of the concept classes of singletons and of half intervals in homogeneous Euclidean half spaces.
Journal ArticleDOI
Tractability of the Approximation of High-Dimensional Rank One Tensors
Erich Novak,Daniel Rudolf +1 more
TL;DR: In this article, the authors study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms, and show that for certain parameters (smoothness and norm of the $$ r$$ th derivative), this problem is intractable, while for other parameters, the problem is tractable and the complexity is only polynomial in the dimension for every fixed ǫ > 0.
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.