Volume 1314 of the series Lecture Notes in Computer Science pp 358376
Learning from positive data
 Stephen MuggletonAffiliated withOxford University Computing Laboratory
Abstract
Gold showed in 1967 that not even regular grammars can be exactly identified from positive examples alone. Since it is known that children learn natural grammars almost exclusively from positives examples, Gold's result has been used as a theoretical support for Chomsky's theory of innate human linguistic abilities. In this paper new results are presented which show that within a Bayesian framework not only grammars, but also logic programs are learnable with arbitrarily low expected error from positive examples only. In addition, we show that the upper bound for expected error of a learner which maximises the Bayes' posterior probability when learning from positive examples is within a small additive term of one which does the same from a mixture of positive and negative examples. An Inductive Logic Programming implementation is described which avoids the pitfalls of greedy search by global optimisation of this function during the local construction of individual clauses of the hypothesis. Results of testing this implementation on artificiallygenerated datasets are reported. These results are in agreement with the theoretical predictions.
 Title
 Learning from positive data
 Book Title
 Inductive Logic Programming
 Book Subtitle
 6th International Workshop, ILP96 Stockholm, Sweden, August 26–28, 1996 Selected Papers
 Pages
 pp 358376
 Copyright
 1997
 DOI
 10.1007/3540634940_65
 Print ISBN
 9783540634942
 Online ISBN
 9783540695837
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1314
 Series Subtitle
 Lecture Notes in Artificial Intelligence
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Stephen Muggleton ^{(1)}
 Author Affiliations

 1. Oxford University Computing Laboratory, OX1 3QD, Parks Road, Oxford, UK
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