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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Journal ArticleDOI
The true sample complexity of active learning
TL;DR: It is proved that it is always possible to learn an ε-good classifier with a number of samples asymptotically smaller than this, which contrasts with the traditional analysis of active learning problems such as non-homogeneous linear separators or depth-limited decision trees, in which Ω(1/ε) lower bounds are common.
Proceedings ArticleDOI
Fat-shattering and the learnability of real-valued functions
TL;DR: It is shown that, given some restrictions on the noise, a function class is learnable in this model if and only if its fat-shattering function is finite, and analogous results in an agnostic setting, where there is no assumption of an underlying function class.
Proceedings ArticleDOI
On the computational complexity of approximating distributions by probabilistic automata
Naoki Abe,Manfred K. Warmuth +1 more
TL;DR: A rigorous performance criterion for training algorithms for probabilistic automata (PAs) and hidden Markov models (HMMs), used extensively for speech recognition, is introduced and the complexity of the training problem as a computational problem is analyzed.
Journal ArticleDOI
Learning pattern classification-a survey
TL;DR: This basic model best illustrates intuition and analysis techniques while still containing the essential features and serving as a prototype for many applications.
Proceedings ArticleDOI
Bounds on the sample complexity of Bayesian learning using information theory and the VC dimension
TL;DR: A systematic investigation and comparison of two fundamental quantities in learning and information theory: the probability of an incorrect prediction for an optimal learning algorithm, and the Shannon information gain is undertaken.
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.