Journal ArticleDOI
Learnability and the Vapnik-Chervonenkis dimension
Reads0
Chats0
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
More filters
Journal ArticleDOI
Hierarchical Cooperation in Ad Hoc Networks: Optimal Clustering and Achievable Throughput
TL;DR: It is found that the hierarchical scheme achieves a scaling with the exponent depending on n, and a clustering algorithm is developed, which divides the whole network into quadrilateral clusters, each with exactly the number of nodes required.
Dissertation
Computational applications of noise sensitivity
Ryan O'Donnell,Madhu Sudan +1 more
TL;DR: The noise sensitivity of various classes of boolean functions, including majorities and recursive majorities, boolean threshold functions, and monotone functions are investigated, and it is shown that any class whose functions have low noise sensitivity is efficiently learnable.
Proceedings ArticleDOI
Data reduction for weighted and outlier-resistant clustering
Dan Feldman,Leonard J. Schulman +1 more
TL;DR: The essential challenge that arises in these optimization problems is data reduction for the weighted k-median problem, and this work solves this problem, which was previously solved only in one dimension ([Har-Peled FSTTCS' 06], [Feldman, Fiat and Sharir FOCS'06]).
Proceedings ArticleDOI
Private PAC learning implies finite Littlestone dimension
TL;DR: It is shown that every approximately differentially private learning algorithm (possibly improper) for a class H with Littlestone dimension d requires Ω(log*(d)) examples, and it follows that the class of thresholds over ℕ can not be learned in a private manner.
Journal ArticleDOI
The Learnability of Description Logics with Equality Constraints
William W. Cohen,Haym Hirsh +1 more
TL;DR: The learnable sublanguage of the restricted first-order logics known as “description logics” appears to be incomparable in expressive power to any subset of first- order logic previously known to be learnable.
References
More filters
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.