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
Citations
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Book ChapterDOI
Efficient learning with virtual threshold gates
TL;DR: This work reduces learning simple geometric concept classes to learning disjunctions over exponentially many variables and applies an on-line algorithm called Winnow whose number of prediction mistakes grows only logarithmically with the number of variables.
Book ChapterDOI
Approximations by OBDDs and the Variable Ordering Problem
TL;DR: Methods from communication complexity and information theory are combined to prove that the direct storage access function and the inner product function have the following property: they have linear π-OBDD size for some variable ordering π and, for most variable orderings π′ all functions which approximate them on considerably more than half of the inputs, need exponential τ′-OB DD size.
Journal ArticleDOI
Neural networks and some applications to finance
K. Feldman,J. Kingdon +1 more
TL;DR: This paper offers an introduction and overview to neural nets with particular emphasis on financial applications, and surveys some of the recent research issues and algorithms used in applying neural nets to real-world problems.
Proceedings Article
Sample Size Requirements for Feedforward Neural Networks
TL;DR: This work seeks to narrow the gap between theory and practice by transforming the problem into determining the distribution of the supremum of a random field in the space of weight vectors, which is attacked by application of a recent technique called the Poisson clumping heuristic.
Journal ArticleDOI
Exact VC-dimension of Boolean monomials
TL;DR: It is shown that the Vapnik-Chervonenkis dimension of Boolean monomials over n variables is at most n for all n ⩾ 2 and is equal to the VC-dimension of the proper subclass of monotonemonomials.
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.