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
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Posted Content
Quantum versus Classical Learnability
TL;DR: This work considers quantum versions of two well-studied models of learning Boolean functions: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples to establish a polynomial relationship between the number of quantum versus classical queries required for learning.
Proceedings Article
FONN: Combining First Order Logic with Connectionist Learning
TL;DR: The primary goal is to bring into a neural network architecture the capability of dealing with structured data of unrestricted size, by allowing to dynamically bind the classiication rules to diierent items occurring in the input data.
Proceedings ArticleDOI
A role of total margin in support vector machines
TL;DR: The total margin algorithm which considers the distance between all data points and the separating hyperplane is suggested, which extends existing support vector machine algorithms and improves the generalization error bound.
Journal ArticleDOI
On the practical applicability of VC dimension bounds
Sean B. Holden,Mahesan Niranjan +1 more
TL;DR: The more recent Vapnik-Chervonenkis dimension-based bounds on sample complexity provide sample complexity predictions that are significantly more applicable in practice than those provided by earlier theories; however, it is found that these theories still have significant shortcomings.
Journal ArticleDOI
A Bound on the Precision Required to Estimate a Boolean Perceptron from Its Average Satisfying Assignment
TL;DR: The result provides a mildly superpolynomial upper bound on the growth rate of the sample size required to learn Boolean perceptrons in the "restricted focus of attention" setting and finds some interesting geometrical properties of the vertices of the unit hypercube.
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.