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
Optimal quantum sample complexity of learning algorithms
TL;DR: In this paper, it was shown that quantum and classical sample complexity are in fact equal up to constant factors in both the PAC and agnostic models, where each example is a coherent quantum state.
Book ChapterDOI
On the Learnability of Hidden Markov Models
TL;DR: A simple result is presented that links the learning of hidden Markov models to results in complexity theory about nonlearnability of finite automata under certain cryptographic assumptions.
Journal ArticleDOI
Training digital circuits with Hamming clustering
Marco Muselli,Diego Liberati +1 more
TL;DR: A theoretical evaluation of the execution time required by Hamming clustering shows that the behavior of the computational cost is polynomial, and extensive simulations on artificial and real-world benchmarks point out also the generalization ability of the logical networks trained by HC.
Proceedings ArticleDOI
On real Turing machines that toss coins
TL;DR: It is shown that the classes BPP, PP, PH, and PSPACE are not enlarged by allowing the use of real constants and arithmetic at unit cost provided the authors restrict branching to equality tests.
Book ChapterDOI
Learnability of bipartite ranking functions
Shivani Agarwal,Dan Roth +1 more
TL;DR: A model of learnability for ranking functions in a particular setting of the ranking problem known as the bipartite ranking problem is defined, and a number of results in this model are derived.
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.