Encyclopedia of the Sciences of Learning

2012 Edition
| Editors: Norbert M. Seel

Approximative Learning Vs. Inductive Learning

  • Henning FernauEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1428-6_555

Synonyms

Definition

As explained below, there is no unique definition of this term available. Vaguely speaking, any learner that is not aiming at the definite, exact identification of a concept, but is rather content with obtaining (learning) a concept that comes close to the target may be termed approximative.

Theoretical Background

In the (mathematical) theory of learning, the term approximative learning is used in different meanings. To ease understanding the concepts, briefly recall what inductive learning means: upon receiving (positive or negative) evidence, the learner (often also called inference machine) formulates hypotheses that should, over time, (always) yield a correct one. This notion goes at least back to Gold, 1967. This concept leads to several natural questions:
  1. 1.

    What is a “correct hypothesis?” This can be answered on a purely syntactic level (leading, e.g., to the notion of EX[planatory]-learning) or on a more semantic level (behaviorally...

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References

  1. Gold, E. M. (1967). Language identification in the limit. Information and Control, 10, 447–474.Google Scholar
  2. Kobayashi, S., & Yokomori, T. (1995). On approximately identifying concept classes in the limit. In K. P. Jantke, T. Shinohara, & Th. Zeugmann (Eds.), Algorithmic learning theory ALT’95, LNAI 997 (pp. 298–312). Berlin/Heidelberg: Springer.Google Scholar
  3. Kobayashi, S., & Yokomori, T. (1997). Learning approximately regular languages with reversible languages. Theoretical Computer Science, 174(1–2), 251–257.Google Scholar
  4. Menzel, W., Stephan, F., et al. (2003). Inductive versus approximative learning. In R. Kuehn (Ed.), Perspectives of adaptivity and learning (pp. 187–209). Berlin/Heidelberg: Springer.Google Scholar
  5. Valiant, L. G. (1984). A theory of the learnable. Communications of the ACM, 27, 1134–1142.Google Scholar
  6. Vidyasagar, M. (1997). A theory of learning and generalization, with applications to neural networks and control systems. London: Springer.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Abteilung Informatik und Wirtschaftsinformatik, Universität TrierTrierGermany