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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Journal ArticleDOI
Learning Long-Distance Phonotactics
TL;DR: This article showed that specific properties of long-distance phonotactic patterns derived from consonantal harmony patterns (Hansson 2001, Rose and Walker 2004) follow from a learner that generalizes only on the basis of the order of sounds, not the distance between them.
Journal ArticleDOI
On Limited Nondeterminism and the Complexity of the V-C Dimension
TL;DR: This work characterize precisely the complexity of several natural computational problems in NP, which have been proposed but not categorized satisfactorily in the literature: Computing the Vapnik?Chervonenkis dimension of a 0?1 matrix; finding the minimum dominating set of a tournament; satisfying a Boolean expression by perturbing the default truth assignment; and several others.
Proceedings ArticleDOI
Learning Geometric Concepts via Gaussian Surface Area
TL;DR: Gaussian surface area essentially characterizes the computational complexity of learning under the Gaussian distribution, and this is the first subexponential time algorithm for learning general convex sets even in the noise-free (PAC) model.
Journal ArticleDOI
A discriminative model for semi-supervised learning
Maria-Florina Balcan,Avrim Blum +1 more
TL;DR: An augmented version of the PAC model designed for semi-supervised learning is described, that can be used to reason about many of the different approaches taken over the past decade in the Machine Learning community and provides a unified framework for analyzing when and why unlabeled data can help, in which one can analyze both sample-complexity and algorithmic issues.
Proceedings Article
On the Difficulty of Approximately Maximizing Agreements
TL;DR: For a variety of common concept classes, it is proved that, unless P=NP, there is no polynomial time approximation scheme for finding a member in the class that approximately maximizes the agreement with a given training sample.
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.