Please use this identifier to cite or link to this item: https://doi.org/10.1007/978-3-642-34106-9_7
Title: Enlarging learnable classes
Authors: Jain, S. 
Kötzing, T.
Stephan, F. 
Issue Date: 2012
Source: Jain, S.,Kötzing, T.,Stephan, F. (2012). Enlarging learnable classes. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 7568 LNAI : 36-50. ScholarBank@NUS Repository. https://doi.org/10.1007/978-3-642-34106-9_7
Abstract: An early result in inductive inference shows that the class of Ex-learnable sets is not closed under unions. In this paper we are interested in the following question: For what classes of functions is the union with an arbitrary Ex-learnable class again Ex-learnable, either effectively (in an index for a learner of an Ex-learnable class) or non-effectively? We show that the effective case and the non-effective case separate, and we give a sufficient criterion for the effective case. Furthermore, we extend our notions to considering unions with classes of single functions, as well as to other learning criteria, such as finite learning and behaviorally correct learning. Furthermore, we consider the possibility of (effectively) extending learners to learn (infinitely) more functions. It is known that all Ex-learners learning a dense set of functions can be effectively extended to learn infinitely more. It was open whether the learners learning a non-dense set of functions can be similarly extended. We show that this is not possible, but we give an alternative split of all possible learners into two sets such that, for each of the sets, all learners from that set can be effectively extended. We analyze similar concepts also for other learning criteria. © 2012 Springer-Verlag.
Source Title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
URI: http://scholarbank.nus.edu.sg/handle/10635/43287
ISBN: 9783642341052
ISSN: 03029743
DOI: 10.1007/978-3-642-34106-9_7
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