Journal ArticleDOI
Learnability and the Vapnik-Chervonenkis dimension
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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
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Book ChapterDOI
Repairing Decision-Making Programs Under Uncertainty
TL;DR: In this paper, the authors propose distribution-guided inductive synthesis, a repair technique that iteratively samples a finite set of inputs from a probability distribution defining the precondition, synthesizes a minimal repair to the program over the sampled inputs using an smt-based encoding, and verifies that the resulting program is correct and is semantically close to the original program.
Proceedings ArticleDOI
PAC-like upper bounds for the sample complexity of leave-one-out cross-validation
TL;DR: This paper addresses the following question: if the authors have n training examples what is the probability that the leave-one-out cross-validation estimate differs from the actual error probability by more than a constant c?
Book ChapterDOI
Learning and decision-making in the framework of fuzzy lattices
TL;DR: A novel theoretical framework is delineated for supervised and unsupervised learning, called framework of fuzzy lattices, which suggests mathematically sound tools for dealing separately and/or jointly with disparate types of data including vectors of numbers, fuzzy sets, symbols, etc.
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.