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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.

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Journal ArticleDOI

The minimum feature set problem

TL;DR: The VC dimension of the set of linear-threshold functions that have nonzero weights for at most s of n inputs is bound, showing that the problem of minimizing the number of nonzero input weights used is both NP-hard and difficult to approximate.
Journal ArticleDOI

Estimates of storage capacity of multilayer perceptron with threshold logic hidden units

TL;DR: The storage capacity of multilayer perceptron with n inputs, h(1) threshold logic units in the first hidden layer and 1 output is estimated and it is shown that such a network has memory capacity between nh(1)+1 and 2(nh( 1)+1) input patterns and for the most efficient networks in this class between 1 and 2 input patterns per connection.
Journal ArticleDOI

A framework for polynomial-time query learnability

TL;DR: The purpose of this paper is to prepare a formal framework for studying “polynomial-time” query learnability, and introduces necessary notation and clarify notions that are necessary for discussing polynomial-time query learning.
Journal ArticleDOI

On the Quantum versus Classical Learnability of Discrete Distributions

TL;DR: The primary result is the explicit construction of a class of discrete probability distributions which, under the decisional Diffie-Hellman assumption, is provably not efficiently PAC learnable by a classical generative modelling algorithm, but for which an efficient quantum learner is constructed.
Journal Article

Multiple-instance learning from distributions

TL;DR: A new theoretical framework for analyzing the multiple-instance learning (MIL) setting is proposed and it is shown that it is possible to learn accurate instance - and bag-labeling functions in this setting as well as functions that correctly rank bags or instances under weak assumptions.
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.
Book

Pattern classification and scene analysis

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.