Trading monotonicity demands versus mind changes

  • Steffen Lange
  • Thomas Zeugmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 904)

Abstract

The present paper deals with with the learnability of indexed families \({\cal L}\) of uniformly recursive languages from positive data. We consider the influence of three monotonicity demands to the efficiency of the learning process. The efficiency of learning is measured in dependence on the number of mind changes a learning algorithm is allowed to perform. The three notions of monotonicity reflect different formalizations of the requirement that the learner has to produce better and better generalizations when fed more and more data on the target concept.

We distinguish between exact learnability (\({\cal L}\) has to be inferred with respect to \({\cal L}\)), class preserving learning (\({\cal L}\) has to be inferred with respect to some suitable chosen enumeration of all the languages from \({\cal L}\)), and class comprising inference (\({\cal L}\) has to be learned with respect to some suitable chosen enumeration of uniformly recursive languages containing at least all the languages from \({\cal L}\)).

In particular, we prove that a relaxation of the relevant monotonicity requirement may result in an arbitrarily large speed-up.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Angluin, D. (1980), Inductive inference of formal languages from positive data, Information and Control, 45 (1980), 117–135.Google Scholar
  2. Barzdin, Ya.M., and Freivalds, R.V. (1972), On the prediction of general recursive functions, Sov. Math. Dokl. 13, 1224–1228.Google Scholar
  3. Barzdin, Ya.M., Kinber, E.B., and Podnieks, K.M. (1974), Об ускорении синтеза и прогнозирования φункций, in “Теория Алгоритмов и Программ,” Vol. 1 (Ya.M. Barzdin, Ed.) Latvian State University, Riga, pp. 117–128.Google Scholar
  4. Case, J., and Smith, C.H. (1983), Comparison of identification criteria for machine inductive inference, Theoretical Computer Science25, 193–220.Google Scholar
  5. Gasarch, W.I., and Velauthapillai, M. (1992), Asking questions versus verifiability, in “Proceedings 3rd International Workshop on Analogical and Inductive Inference,” (K.P. Jantke, ed.) Lecture Notes in Artificial Intelligence Vol. 642, pp. 197–213, Springer-Verlag, Berlin.Google Scholar
  6. Gold, M.E. (1967), Language identification in the limit, Information and Control10, 447–474.Google Scholar
  7. Hopcroft, J.E., and Ullman, J.D. (1969), “Formal Languages and their Relation to Automata,” Addison-Wesley, Reading, Massachusetts.Google Scholar
  8. Jantke, K.P. (1991), Monotonic and non-monotonic inductive inference, New Generation Computing8, 349–360.Google Scholar
  9. Kapur, S., and Bilardi, G. (1992), Language learning without overgeneralization, in “Proceedings 9th Annual Symposium on Theoretical Aspects of Computer Science,” (A. Finkel and M. Jantzen, Eds.), Lecture Notes in Computer Science Vol. 577, pp. 245–256, Springer-Verlag, Berlin.Google Scholar
  10. Kinber, E.B. (1994), Monotonicity versus efficiency for learning languages from texts, in “Proceedings 5th Workshop on Algorithmic Learning Theory,” (S. Arikawa and K.P. Jantke, Eds.), Lecture Notes in Artificial Intelligence Vol. 872, pp. 395–406.Google Scholar
  11. Lange, S. (1994), The representation of recursive languages and its impact on the efficiency of learning, in “Proceedings 7th Annual ACM Conference on Computational Learning Theory, New Brunswick, July 1994,” pp. 256–267, ACM Press, New York.Google Scholar
  12. Lange, S., and Zeugmann, T. (1993a), Monotonic versus non-monotonic language learning, in “Proceedings 2nd International Workshop on Non-monotonic and Inductive Logic, December 1991, Reinhardsbrunn,” (G. Brewka, K.P. Jantke and P.H. Schmitt, Eds.), Lecture Notes in Artificial Intelligence Vol. 659, pp. 254–269, Springer-Verlag, Berlin.Google Scholar
  13. Lange, S., and Zeugmann, T. (1993b), Learning recursive languages with bounded mind changes, International Journal of Foundations of Computer Science4, 157–178.Google Scholar
  14. Lange, S., and Zeugmann, T. (1993c), Language learning in dependence on the space of hypotheses, in “Proceedings 6th Annual ACM Conference on Computational Learning Theory,” pp. 127–136, ACM Press, New York.Google Scholar
  15. Lange, S., and Zeugmann, T. (1994), Trading monotonicity demands versus efficiency, Bulletin of Informatics and Cybernetics, to appear.Google Scholar
  16. Lange, S., Zeugmann, T., and Kapur, S. (1994), Monotonic and dual-monotonic language learning, Theoretical Computer Science, to appear.Google Scholar
  17. Machtey, M., and Young, P. (1978), “An Introduction to the General Theory of Algorithms,” North-Holland, New York.Google Scholar
  18. Mukouchi, Y. (1992), Inductive inference with bounded mind changes, in “Proceedings 3rd Workshop on Algorithmic Learning Theory,” Tokyo, Japan, JSAI, pp. 125–134.Google Scholar
  19. Mukouchi, Y. (1994), Inductive inference of recursive concepts, Ph.D. Thesis, R1FIS, Kyushu University 33, RIFIS-TR-CS-82, March 25th.Google Scholar
  20. Osherson, D., Stob, M., and Weinstein, S. (1986), “Systems that Learn, An Introduction to Learning Theory for Cognitive and Computer Scientists,” MIT-Press, Cambridge, Massachusetts.Google Scholar
  21. Shinohara, T. (1990), Inductive Inference from Positive Data is Powerful, in “Proc. 3rd Annual Workshop on Computational Learning Theory,” pp. 97–110, Morgan Kaufmann Publishers Inc.Google Scholar
  22. Wiehagen, R. (1991), A thesis in inductive inference, in “Proceedings First International Workshop on Nonmonotonic and Inductive Logic,” (J. Dix, K.P. Jantke and P.H. Schmitt, Eds.), Lecture Notes in Artificial Intelligence 543, pp. 184–207, Springer-Verlag, Berlin.Google Scholar
  23. Wiehagen, R., and Zeugmann, T. (1994), Ignoring data may be the only way to learn efficiently, Journal Experimental and Theoretical Artificial Intelligence6, 131–144.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Steffen Lange
    • 1
  • Thomas Zeugmann
    • 2
  1. 1.FB Mathematik und InformatikHTWK LeipzigLeipzig
  2. 2.Research Institute of Fundamental Information ScienceKyushu University 33FukuokaJapan

Personalised recommendations