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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Deep Learning
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Neural networks for pattern recognition
TL;DR: This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition, and is designed as a text, with over 100 exercises, to benefit anyone involved in the fields of neural computation and pattern recognition.
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Advances in kernel methods: support vector learning
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An overview of statistical learning theory
TL;DR: How the abstract learning theory established conditions for generalization which are more general than those discussed in classical statistical paradigms are demonstrated and how the understanding of these conditions inspired new algorithmic approaches to function estimation problems are demonstrated.
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Understanding Machine Learning: From Theory To Algorithms
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References
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Proceedings ArticleDOI
A general lower bound on the number of examples needed for learning
TL;DR: This paper proves a lower bound on the number of random examples required for distribution-free learning of a concept class C and shows that for many interesting concept classes, including k CNF and k DNF, the bound is actually tight to within a constant factor.
Journal ArticleDOI
A general lower bound on the number of examples needed for learning
TL;DR: In this paper, a lower bound of Ω ((1/∆)ln(1/δ)+VCdim(C )/ε) was shown for distribution-free learning of a concept class C, where VCdim( C ) is the Vapnik-Chervonenkis dimension and ǫ and à are the accuracy and confidence parameters.
Proceedings ArticleDOI
Epsilon-nets and simplex range queries
David Haussler,Emo Welzl +1 more
TL;DR: A new technique for half-space and simplex range query using random sampling to build a partition-tree structure and introduces the concept of anε-net for an abstract set of ranges to describe the desired result of this random sampling.
Proceedings ArticleDOI
Learning in the presence of malicious errors
Michael Kearns,Ming Li +1 more
TL;DR: A practical extension to the Valiant model of machine learning from examples, where the presence of errors, possibly maliciously generated by an adversary, in the sample data is studied to preserve an error-free oracle for examples of the function being learned.