Advertisement

Intrinsic Complexity of Uniform Learning

  • Sandra Zilles
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2842)

Abstract

Inductive inference is concerned with algorithmic learning of recursive functions. In the model of learning in the limit a learner successful for a class of recursive functions must eventually find a program for any function in the class from a gradually growing sequence of its values. This approach is generalized in uniform learning, where the problem of synthesizing a successful learner for a class of functions from a description of this class is considered.

A common reduction-based approach for comparing the complexity of learning problems in inductive inference is intrinsic complexity. In this context, reducibility between two classes is expressed via recursive operators transforming target functions in one direction and sequences of corresponding hypotheses in the other direction.

The present paper is the first one concerned with intrinsic complexity of uniform learning. The relevant notions are adapted and illustrated by several examples. Characterizations of complete classes finally allow for various insightful conclusions. The connection to intrinsic complexity of non-uniform learning is revealed within several analogies concerning firstly the role and structure of complete classes and secondly the general interpretation of the notion of intrinsic complexity.

Keywords

Initial Segment Recursive Function Inductive Inference Recursive Operator Hypothesis Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baliga, G., Case, J., Jain, S.: The synthesis of language learners. Information and Computation 152, 16–43 (1999)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Blum, L., Blum, M.: Toward a mathematical theory of inductive inference. Information and Control 28, 125–155 (1975)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Case, J., Smith, C.: Comparison of identification criteria for machine inductive inference. Theoretical Computer Science 25, 193–220 (1983)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Freivalds, R., Kinber, E., Smith, C.: On the intrinsic complexity of learning. Information and Computation 123, 64–71 (1995)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Garey, M., Johnson, D.: Computers and Intractability – A Guide to the Theory of NP-Completeness. Freeman and Company, New York (1979)MATHGoogle Scholar
  6. 6.
    Gold, E.M.: Limiting recursion. Journal of Symbolic Logic 30, 28–48 (1965)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gold, E.M.: Language identification in the limit. Information and Control 10, 447–474 (1967)MATHCrossRefGoogle Scholar
  8. 8.
    Jain, S., Kinber, E., Papazian, C., Smith, C., Wiehagen, R.: On the intrinsic complexity of learning recursive functions. Information and Computation 184, 45–70 (2003)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Jain, S., Kinber, E., Wiehagen, R.: Language learning from texts: Degrees of intrinsic complexity and their characterizations. In: Proc. 13th Annual Conference on Computational Learning Theory, pp. 47–58. Morgan Kaufmann, San Francisco (2000)Google Scholar
  10. 10.
    Jain, S., Sharma, A.: The intrinsic complexity of language identification. Journal of Computer and System Sciences 52, 393–402 (1996)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Jain, S., Sharma, A.: The structure of intrinsic complexity of learning. Journal of Symbolic Logic 62, 1187–1201 (1997)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Jantke, K.P.: Natural properties of strategies identifying recursive functions. Elektronische Informationsverarbeitung und Kybernetik 15, 487–496 (1979)MATHMathSciNetGoogle Scholar
  13. 13.
    Kapur, S., Bilardi, G.: On uniform learnability of language families. Information Processing Letters 44, 35–38 (1992)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Osherson, D., Stob, M., Weinstein, S.: Synthesizing inductive expertise. Information and Computation 77, 138–161 (1988)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Rogers, H.: Theory of Recursive Functions and Effective Computability. MIT Press, Cambridge (1987)Google Scholar
  16. 16.
    Zilles, S.: On the synthesis of strategies identifying recursive functions. In: Helmbold, D.P., Williamson, B. (eds.) COLT 2001 and EuroCOLT 2001. LNCS (LNAI), vol. 2111, pp. 160–176. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Zilles, S.: On the comparison of inductive inference criteria for uniform learning of finite classes. In: Abe, N., Khardon, R., Zeugmann, T. (eds.) ALT 2001. LNCS (LNAI), vol. 2225, pp. 251–266. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sandra Zilles
    • 1
  1. 1.FB InformatikUniversität KaiserslauternKaiserslauternGermany

Personalised recommendations