Input-Dependence in Function-Learning

  • Sanjay Jain
  • Eric Martin
  • Frank Stephan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)

Abstract

In the standard literature on inductive inference, a learner sees as input the course of values of the function to be learned. In the present work, it is investigated how reasonable this choice is and how sensitive the model is with respect to variations like the overgraph or undergraph of the function. Several implications and separations are shown and for the basic notions, a complete picture is obtained. Furthermore, relations to oracles, additional information and teams are explored.

Keywords

Inductive inference recursion theory various forms of input presentation team learning learning with additional information 

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References

  1. 1.
    Adleman, L., Blum, M.: Inductive inference and unsolvability. Journal of Symbolic Logic 56, 891–900 (1991)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45, 117–135 (1980)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Blum, L., Blum, M.: Towards a mathematical theory of inductive inference. Information and Control 28, 125–155 (1975)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Fortnow, L., Gasarch, W., Jain, S., Kinber, E., Kummer, M., Kurtz, S., Pleszkoch, M., Slaman, T., Solovay, R., Stephan, F.: Extremes in the degrees of inferability. Annals of Pure. and Applied Logic 66, 231–276 (1994)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gold, M.: Language identification in the limit. Information and Control 10, 447–474 (1967)MATHCrossRefGoogle Scholar
  6. 6.
    Jain, S., Sharma, A.: On the non-existence of maximal inference degrees for language identification. Information Processing Letters 47, 81–88 (1993)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Jain, S., Sharma, A.: Computational limits on team identification of languages. Information and Computation 130(1), 19–60 (1996)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kummer, M., Stephan, F.: On the structure of degrees of inferability. Journal of Computer and System Sciences, Special Issue COLT (1993) 52, 214–238 (1996)MathSciNetGoogle Scholar
  9. 9.
    Odifreddi, P.: Classical Recursion Theory. North-Holland, Amsterdam (1989)MATHGoogle Scholar
  10. 10.
    Osherson, D., Stob, M., Weinstein, S.: Systems That Learn, An Introduction to Learning Theory for Cognitive and Computer Scientists. In: Bradford, The MIT Press, Cambridge, Massachusetts (1986)Google Scholar
  11. 11.
    Pitt, L., Smith, C.H.: Probability and plurality for aggregations of learning machines. Information and Computation 77, 77–92 (1988)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Soare, R.: Recursively Enumerable Sets and Degrees. A Study of Computable Functions and Computably Generated Sets. Springer, Heidelberg (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sanjay Jain
    • 1
  • Eric Martin
    • 2
  • Frank Stephan
    • 3
  1. 1.Department of Computer Science, National University of Singapore, Singapore 117543Republic of Singapore
  2. 2.Department of Computer Science and Engineering, The University of New South Wales, Sydney 2052, NSWCommonwealth of Australia
  3. 3.Department of Mathematics, National University of Singapore, Singapore 117543Republic of Singapore

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