Communications of the ACM
Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Learnability by fixed distributions
COLT '88 Proceedings of the first annual workshop on Computational learning theory
Testing geometric objects
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Testing as a dual to learning
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
DNF—if you can't learn'em, teach'em: an interactive model of teaching
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
A Boolean measure of similarity
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
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A model for approximate testing of concepts, which relates to the PAC model of learning, has been developed. In this model an approximate testing algorithm produces a finite set of examples that distinguishes one concept from others that differ from it by more than a given error bound. This model corresponds closely to the helpful teacher learning model. In this paper we examine properties of a concept class that make it testable or untestable. We define a new measure that is a dual to the VC-dimension, called the testing dimension of a concept class, and show how it yields untestability results for certain concept classes.