Encyclopedia of Machine Learning

2010 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Stochastic Finite Learning

  • Thomas Zeugmann
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30164-8_787

Motivation and Background

Assume that we are given a concept class \(\mathcal{C}\)

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Recommended Reading

  1. Angluin, D. (1980a). Finding patterns common to a set of strings. Journal of Computer and System Sciences, 21(1), 46–62.MathSciNetzbMATHCrossRefGoogle Scholar
  2. Angluin, D. (1980b). Inductive inference of formal languages from positive data. Information Control, 45(2), 117–135.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Blumer, A., Ehrenfeucht, A., Haussler, D., & Warmuth, M. K. (1989). Learnability and the Vapnik–Chervonenkis dimension. Journal of the ACM, 36(4), 929–965.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Erlebach, T., Rossmanith, P., Stadtherr, H., Steger, A., & Zeugmann, T. (2001). Learning one-variable pattern languages very efficiently on average, in parallel, and by asking queries. Theoretical Computer Science, 261(1), 119–156.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Gold, E. M. (1967). Language identification in the limit. Information and Control, 10(5), 447–474.zbMATHCrossRefGoogle Scholar
  6. Haussler, D. (1987). Bias, version spaces and Valiant’s learning framework. In P. Langley (Ed.), Proceedings of the fourth international workshop on machine learning (pp. 324–336). San Mateo, CA: Morgan Kaufmann.Google Scholar
  7. Haussler, D., Kearns, M., Littlestone, N., & Warmuth, M. K. (1991). Equivalence of models for polynomial learnability. Information and Computation, 95(2), 129–161.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Lange, S., & Wiehagen, R. (1991). Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8(4), 361–370.zbMATHCrossRefGoogle Scholar
  9. Lange, S., & Zeugmann, T. (1996). Set-driven and rearrangement-independent learning of recursive languages. Mathematical Systems Theory, 29(6), 599–634.MathSciNetzbMATHGoogle Scholar
  10. Mitchell, A., Scheffer, T., Sharma, A., & Stephan, F. (1999). The VC-dimension of sub- classes of pattern languages. In O. Watanabe & T. Yokomori (Eds.), Algorithmic learning theory, tenth international conference, ALT”99, Tokyo, Japan, December 1999, Proceedings, Lecture notes in artificial intelligence (Vol. 1720, pp. 93–105). Springer.Google Scholar
  11. Reischuk, R., & Zeugmann, T. (2000). An average-case optimal one-variable pattern language learner. Journal of Computer and System Sciences, 60(2), 302–335.MathSciNetzbMATHCrossRefGoogle Scholar
  12. Rossmanith, P., & Zeugmann, T. (2001). Stochastic finite learning of the pattern languages. Machine Learning, 44(1/2), 67–91.zbMATHCrossRefGoogle Scholar
  13. Saly, A., Goldman, M. J. K., & Schapire, R. E. (1993). Exact identification of circuits using fixed points of amplification functions. SIAM Journal of Computing, 22(4), 705–726.CrossRefGoogle Scholar
  14. Valiant, L. G. (1984). A theory of the learnable. Communications of the ACM, 27(11), 1134–1142.zbMATHCrossRefGoogle Scholar
  15. Zeugmann, T. (1998). Lange and Wiehagen’s pattern language learning algorithm: An average-case analysis with respect to its total learning time. Annals of Mathematics and Artificial Intelligence, 23, 117–145.MathSciNetzbMATHCrossRefGoogle Scholar
  16. Zeugmann, T. (2006). From learning in the limit to stochastic finite learning. Theoretical Computer Science, 364(1), 77–97. Special issue for ALT 2003.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Thomas Zeugmann

There are no affiliations available