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
Computing with Spiking Neuron Networks
TL;DR: This chapter relates theory of the “spiking neuron” in Section 1 and summarizes the most currently-in-use models of neurons and synaptic plasticity in Section 2, and addresses the computational power and problem of learning in networks of spiking neurons.
ReportDOI
Neural Network Exploration Using Optimal Experiment Design
TL;DR: In this article, the problem of learning input/output mappings through exploration is considered, e.g. learning the kinematics or dynamics of a robotic manipulator, and results from the field of optimal experiment design are used to guide such exploration.
Proceedings ArticleDOI
On the learnability of discrete distributions
TL;DR: A new model of learning probability distributions from independent draws is introduced, inspired by the popular Probably Approximately Correct (PAC) model for learning boolean functions from labeled examples, in the sense that it emphasizes efficient and approximate learning, and it studies the learnability of restricted classes of target distributions.
Proceedings ArticleDOI
Weakly learning DNF and characterizing statistical query learning using Fourier analysis
TL;DR: It is proved that an algorithm due to Kushilevitz and Mansour can be used to weakly learn DNF using membership queries in polynomial time, with respect to the uniform distribution on the inputs, and it is obtained that DNF expressions and decision trees are not evenWeakly learnable with any unproven assumptions.
Journal ArticleDOI
Ambiguous chance constrained problems and robust optimization
Emre Erdogan,Garud Iyengar +1 more
TL;DR: The robust sampled problem is shown to be a good approximation for the ambiguous chance constrained problem with a high probability using the Strassen-Dudley Representation Theorem that states that when the distributions of two random variables are close in the Prohorov metric one can construct a coupling of the random variables such that the samples are close with ahigh probability.
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.