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
Learnability can be undecidable
TL;DR: The main idea is to prove an equivalence between learnability and compression, and it is shown that, in some cases, a solution to the ‘estimating the maximum’ problem is equivalent to the continuum hypothesis.
Posted Content
A Survey of Quantum Learning Theory
TL;DR: The main results known for three models of learning are described: exact learning from membership queries, and Probably Approximately Correct (PAC) and agnostic learning from classical or quantum examples.
Journal ArticleDOI
Query-preserving watermarking of relational databases and Xml documents
TL;DR: It is shown that unrestricted databases can not be watermarked while preserving trivial parametric queries, and query languages and classes of structures that allow guaranteed watermarking capacity are exhibited, namely local query languages on structures with bounded degree Gaifman graph, and monadic second-order queries on trees or treelike structures.
Journal ArticleDOI
Using the doubling dimension to analyze the generalization of learning algorithms
TL;DR: Borders on the sample complexity of PAC learning in terms of the doubling dimension of this metric are proved and a bound that holds for any algorithm that outputs a classifier with zero error whenever this is possible is proved.
Proceedings ArticleDOI
Reductions among prediction problems: on the difficulty of predicting automata
Leonard Pitt,Manfred K. Warmuth +1 more
TL;DR: A notion of prediction-preserving reducibility is developed, and it is shown that if DFAs are predictable, then so are all languages in logspace and the predictability of all Booleman formulas.
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.