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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Proceedings ArticleDOI
Discrepancy and in -approximations for bounded VC-dimension
TL;DR: It is shown that if for any m-point subset Y contained in X the number of distinct subsets induced by R on Y is bounded by O(m/sup d/) for a fixed integer d, then there is a coloring with discrepancy at most O(n/sup 1/2-1/2d/ n), implying improved upper bounds on the size of in -approximations for (X, R.
Journal ArticleDOI
The learnability of unknown quantum measurements
TL;DR: In the context of machine learning, the sample complexity problem as mentioned in this paper investigates how many samples (e.g., the size of the training data set) are required to bound the generalization error.
Book ChapterDOI
Epsilon-Nets and Computational Geometry
TL;DR: This chapter presents some results from the theory of range spaces of finite VC-dimension, and introduces canonical geometric range spaces and indicates how other range spaces encountered in computational geometry can be embedded into the canonical ones.
Journal ArticleDOI
Function Learning from Interpolation
Martin Anthony,Peter L. Bartlett +1 more
TL;DR: A characterization of function classes that have this property, in terms of their ‘fat-shattering function’, is derived, a notion that has proved useful in computational learning theory.
Proceedings ArticleDOI
A learning algorithm for elementary formal systems and its experiments on identification of transmembrane domains
TL;DR: The authors have implemented the algorithm for identifying transmembrane domains in amino acid sequences using an elementary formal system and restrict candidate hypotheses to EFSs defined by collections of regular patterns.
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.