Iterative Learning from Positive Data and Negative Counterexamples
A model for learning in the limit is defined where a (so-called iterative) learner gets all positive examples from the target language, tests every new conjecture with a teacher (oracle) if it is a subset of the target language (and if it is not, then it receives a negative counterexample), and uses only limited long-term memory (incorporated in conjectures). Three variants of this model are compared: when a learner receives least negative counterexamples, the ones whose size is bounded by the maximum size of input seen so far, and arbitrary ones. We also compare our learnability model with other relevant models of learnability in the limit, study how our model works for indexed classes of recursive languages, and show that learners in our model can work in non-U-shaped way — never abandoning the first right conjecture.
KeywordsTarget Language Recursive Function Regular Language Positive Data Target Concept
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- [Ang88]Angluin, D.: Queries and concept learning. Machine Learning 2, 319–342 (1988)Google Scholar
- [BCM+05]Baliga, G., Case, J., Merkle, W., Stephan, F., Wiehagen, R.: When unlearning helps (manuscript, 2005), http://www.cis.udel.edu/~case/papers/decisive.ps
- [Bow82]Bowerman, M.: Starting to talk worse: Clues to language acquisition from children’s late speech errors. In: Strauss, S., Stavy, R. (eds.) U-Shaped Behavioral Growth. Developmental Psychology Series. Academic Press, New York (1982)Google Scholar
- [JK06a]Jain, S., Kinber, E.: Iterative learning from positive data and negative counterexamples. Technical Report TRA3/06, School of Computing, National University of Singapore (2006)Google Scholar
- [JK06b]Jain, S., Kinber, E.: Learning languages from positive data and negative counterexamples. Journal of Computer and System Sciences (to appear, 2006)Google Scholar
- [JORS99]Jain, S., Osherson, D., Royer, J., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, 2nd edn. MIT Press, Cambridge (1999)Google Scholar
- [Pop68]Popper, K.: The Logic of Scientific Discovery, 2nd edn. Harper Torch Books, New York (1968)Google Scholar
- [Rog67]Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967); Reprinted by MIT Press in 1987.Google Scholar
- [ZL95]Zeugmann, T., Lange, S.: A guided tour across the boundaries of learning recursive languages. In: Lange, S., Jantke, K.P. (eds.) GOSLER 1994. LNCS (LNAI), vol. 961, pp. 190–258. Springer, Heidelberg (1995)Google Scholar