Encyclopedia of Machine Learning and Data Mining

2017 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Stochastic Finite Learning

  • Thomas Zeugmann
Reference work entry
DOI: https://doi.org/10.1007/978-1-4899-7687-1_793

Motivation and Background

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

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. Angluin D (1980a) Finding patterns common to a set of strings. J Comput Syst Sci 21(1):46–62MathSciNetzbMATHCrossRefGoogle Scholar
  2. Angluin D (1980b) Inductive inference of formal languages from positive data. Inf Control 45(2):117–135MathSciNetzbMATHCrossRefGoogle Scholar
  3. Blumer A, Ehrenfeucht A, Haussler D, Warmuth MK (1989) Learnability and the Vapnik-Chervonenkis dimension. J ACM 36(4):929–965MathSciNetzbMATHCrossRefGoogle 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. Theor Comput Sci 261(1):119–156MathSciNetzbMATHCrossRefGoogle Scholar
  5. Gold EM (1967) Language identification in the limit. Inf Control 10(5):447–474MathSciNetzbMATHCrossRefGoogle Scholar
  6. Haussler D (1987) Bias, version spaces and Valiant’s learning framework. In: Langley P (ed) Proceedings of the fourth international workshop on machine learning. Morgan Kaufmann, San Mateo, pp 324–336CrossRefGoogle Scholar
  7. Haussler D, Kearns M, Littlestone N, Warmuth MK (1991) Equivalence of models for polynomial learnability. Inf Comput 95(2):129–161MathSciNetzbMATHCrossRefGoogle Scholar
  8. Lange S, Wiehagen R (1991) Polynomial-time inference of arbitrary pattern languages. New Gener Comput 8(4):361–370zbMATHCrossRefGoogle Scholar
  9. Lange S, Zeugmann T (1996) Set-driven and rearrangement-independent learning of recursive languages. Math Syst Theory 29(6):599–634MathSciNetzbMATHCrossRefGoogle Scholar
  10. Mitchell A, Scheffer T, Sharma A, Stephan F (1999) The VC-dimension of subclasses of pattern languages. In: Watanabe O, Yokomori T (eds) Proceedings of the 10th international conference on algorithmic learning theory, ALT ’99, Tokyo, Dec 1999. Lecture notes in artificial intelligence, vol 1720. Springer, pp 93–105Google Scholar
  11. Reidenbach D (2006) A non-learnable class of E-pattern languages. Theor Comput Sci 350(1):91–102MathSciNetzbMATHCrossRefGoogle Scholar
  12. Reidenbach D (2008) Discontinuities in pattern inference. Theor Comput Sci 397(1–3):166–193MathSciNetzbMATHCrossRefGoogle Scholar
  13. Reischuk R, Zeugmann T (2000) An average-case optimal one-variable pattern language learner. J Comput Syst Sci 60(2):302–335MathSciNetzbMATHCrossRefGoogle Scholar
  14. Rossmanith P, Zeugmann T (2001) Stochastic finite learning of the pattern languages. Mach Learn 44(1/2): 67–91zbMATHCrossRefGoogle Scholar
  15. Goldman SA, Kearns MJ, Schapire RE (1993) Exact identification of read-once formulas using fixed points of amplification functions. SIAM J Comput 22(4):705–726MathSciNetzbMATHCrossRefGoogle Scholar
  16. Valiant LG (1984) A theory of the learnable. Commun ACM 27(11):1134–1142zbMATHCrossRefGoogle Scholar
  17. Zeugmann T (1998) Lange and Wiehagen’s pattern language learning algorithm: an average-case analysis with respect to its total learning time. Ann Math Artif Intell 23:117–145MathSciNetzbMATHCrossRefGoogle Scholar
  18. Zeugmann T (2006) From learning in the limit to stochastic finite learning. Theor Comput Sci 364(1):77–97. Special issue for ALT 2003Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Hokkaido UniversitySapporoJapan