Communications of the ACM
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Computational optimality theory
Computational optimality theory
BOUNDS ON THE SAMPLE COMPLEXITY OF BAYESIAN LEARNING USINGINFORMATION THEORY AND THE VC DIMENSION
BOUNDS ON THE SAMPLE COMPLEXITY OF BAYESIAN LEARNING USINGINFORMATION THEORY AND THE VC DIMENSION
Phonological derivation in optimality theory
COLING '94 Proceedings of the 15th conference on Computational linguistics - Volume 2
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Given a constraint set with k constraints in the framework of Optimality Theory (OT), what is its capacity as a classification scheme for linguistic data? One useful measure of this capacity is the size of the largest data set of which each subset is consistent with a different grammar hypothesis. This measure is known as the Vapnik-Chervonenkis dimension (VCD) and is a standard complexity measure for concept classes in computational learnability theory. In this work, I use the three-valued logic of Elementary Ranking Conditions to show that the VCD of Optimality Theory with k constraints is k-1. Analysis of OT in terms of the VCD establishes that the complexity of OT is a well-behaved function of k and that the 'hardness' of learning in OT is linear in k for a variety of frameworks that employ probabilistic definitions of learnability.