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International Conference on Algorithmic Learning Theory

ALT 2008: Algorithmic Learning Theory pp 434–448Cite as

Numberings Optimal for Learning

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5254))

Abstract

This paper extends previous studies on learnability in non-acceptable numberings by considering the question: for which criteria which numberings are optimal, that is, for which numberings it holds that one can learn every learnable class using the given numbering as hypothesis space. Furthermore an effective version of optimality is studied as well. It is shown that the effectively optimal numberings for finite learning are just the acceptable numberings. In contrast to this, there are non-acceptable numberings [3] which are optimal for finite learning and effectively optimal for explanatory, vacillatory and behaviourally correct learning. The numberings effectively optimal for explanatory learning are the K-acceptable numberings. A similar characterization is obtained for the numberings which are effectively optimal for vacillatory learning. Furthermore, it is studied which numberings are optimal for one and not for another criterion: among the criteria of finite, explanatory, vacillatory and behaviourally correct learning all separations can be obtained; however every numbering which is optimal for explanatory learning is also optimal for consistent learning.

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Author information

Authors and Affiliations

  1. Department of Computer Science, National University of Singapore, Singapore, 117543, Republic of Singapore

    Sanjay Jain

  2. Department of Computer Science and Department of Mathematics, National University of Singapore, Singapore, 117543, Republic of Singapore

    Frank Stephan

Authors
  1. Sanjay Jain
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  2. Frank Stephan
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Editor information

Editors and Affiliations

  1. Computer Science and Engineering, University of California, San Diego, USA

    Yoav Freund

  2. Department of Computer Science and Information Theory, Department of Computer Science and Budapest University of Technology and Economics, Stoczek u. 2, 1521, Budapest, Hungary

    László Györfi

  3. Department of Math., Stat. and Comp. Sci,, University of Illinois, 851 S. Morgan, IL 60607-7045, Chicago, USA

    György Turán

  4. Division of Computer Science, Hokkaido University, N-14, W-9, 060-0814, Sapporo, Japan

    Thomas Zeugmann

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© 2008 Springer-Verlag Berlin Heidelberg

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Jain, S., Stephan, F. (2008). Numberings Optimal for Learning. In: Freund, Y., Györfi, L., Turán, G., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2008. Lecture Notes in Computer Science(), vol 5254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87987-9_35

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  • DOI: https://doi.org/10.1007/978-3-540-87987-9_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87986-2

  • Online ISBN: 978-3-540-87987-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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