Encyclopedia of the Sciences of Learning

2012 Edition
| Editors: Norbert M. Seel

Learning by Eliminating

  • Rūsiņš FreivaldsEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1428-6_765

Synonyms

Definition

Learning by eliminating as proposed by Freivalds et al. (1994a) is a class of methods used in inductive inference, a research area started by Gold (1967). We consider learning where an algorithmic device inputs data and produces a sequence of programs such that this sequence can be interpreted as a correct program consistent with the given data. For Gold (1967) the sequence was supposed to be an infinite sequence such that all of its members (but a finite number of them) equal one correct program. For learning-by-eliminating algorithms the interpretation of the infinite resulting sequence is different. The sequence is to contain all possible programs with one exception. Namely, one correct program is to be missing.

Theoretical Background

Learning by eliminating means the process of removing potential hypotheses from further consideration thereby converging to a unique hypothesis which will never be eliminated. This hypothesis...

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References

  1. Freivalds, R. (1975). On complexity and optimality of computation in the limit. Theory of Algorithms and Programs, Vol. 233, pp. 155–173 (in Russian).Google Scholar
  2. Freivalds, R., & Zeugmann, Th. (1996). Co-learning of recursive languages from positive data (LNCS, Vol. 1181, pp. 122–133). Berlin/Heidelberg: Springer.Google Scholar
  3. Freivalds, R., Karpinski, M., & Smith, C. H. (1994a). Co-learning of total recursive functions. Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory (COLT 1994), ACM, New Brunswick, pp. 190–197.Google Scholar
  4. Freivalds, R., Gobleja, D., Karpinski, M., & Smith, C. H. (1994b). Co-learnability and FIN-identifiability of enumerable classes of total recursive functions (LNCS, Vol. 872, pp. 100–105). Berlin/Heidelberg: Springer.Google Scholar
  5. Freivalds, R., Karpinski, M., Smith, C. H., & Wiehagen, R. (2002). Learning by the process of elimination. Information and Computation, 176(1), 37–50.Google Scholar
  6. Gold, E. M. (1967). Language identification in the limit. Information and Control, 10, 447–474.Google Scholar
  7. Jain, S., Kinber E. B., & Wiehagen, R. (1996). On learning and Co-learning of minimal programs. (LNCS, Vol. 1160, pp. 242–255). Berlin/Heidelberg: Springer.Google Scholar
  8. Jain, S., Kinber, E. B., & Wiehagen, R. (2000). Language learning from texts: Degrees of instrinsic complexity and their characterizations. Proceedings of the Thirteenth Annual Conference on Computational Learning Theory (COLT 2000), Morgan Kaufmann, Palo Alto, pp. 47–58.Google Scholar
  9. Kummer, M. (1995). A learning-theoretic characterization of classes of recursive functions. Information Processing Letters, 54, 205–211.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia