Communications of the ACM
An analytical comparison of some rule-learning programs
Artificial Intelligence
Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
An interference matching technique for inducing abstractions
Communications of the ACM
Induction of concepts in the predicate calculus
IJCAI'75 Proceedings of the 4th international joint conference on Artificial intelligence - Volume 1
Learning disjunction of conjunctions
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
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We study the problem of learning conjunctive concepts from examples on structural domains like the blocks world. nus class of concepts is formally defined and it is shown that even for samples in which each example (positive or negative) is a two-object scene it is NP-complete to determine if there is any concept in this class that is consistent with the sample. We demonstrate how this result affects the feasibility of Mitchell's version space approach and how it shows that it is unlikely that this class of concepts is polynomiaIIy learnable from random examples in the sense of Valiant. On the other hand, we show that this class is polynomially learnable if we allow a larger hypothesis space. This result holds for any fixed number of objects per scene, but the algorithm is not practical unless the number of objects per scene is very small. We also show that heuristic methods for learning from larger scenes are likely to give an accurate hypothesis if they produce a simple hypothesis consistent with a large enough random sample.