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A space-bounded learning algorithm for axis-parallel rectangles

  • Foued Ameur
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 904)

Abstract

We consider the on-line learnability from equivalence queries only of axis-parallel rectangles over the discrete grid {1,..., n} d (BOX n d ). Further we impose the restriction of “k-space-bounded learning”, i.e. the information the learner can store about the history of the learning protocol is restricted to the previous hypothesis and at most k of the examples seen. Our result improves the best known algorithm about learning BOX n d due to Chen and Maass [9]. Their algorithm has learning complexity O(d2 log n) requires space Θ(d2logn) and time Ω(log(d2log n)) for each learning step. We present an on-line learning algorithm for BOX n d with the same learning complexity, time complexity O(d3log n) which is 2d-space-bounded.

Keywords

Learning Algorithm Target Concept Learning Complexity Membership Query Equivalence Query 
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.

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References

  1. 1.
    F. Ameur, P. Fischer, K.U. Höffgen, and F. Meyer auf der Heide. Trial and Error: A New Approach to Space-Bounded Learning. Computational Learning Theory: EURO-COLT '93, pages 133–144, 1993.Google Scholar
  2. 2.
    Foued Ameur. Space-bounded Identification of Halfplanes in the discrete Grid. AAAI-94 Fall Symposium Series, pages 5–8, 1994.Google Scholar
  3. 3.
    Dana Angluin. Queries and Concept Learning. Machine Learning, 2:319–342, 1988.Google Scholar
  4. 4.
    Peter Auer. On-line Learning of Rectangles in Noisy Environments. Proceedings of the 6th Annual Workshop on Computational Learning Theory, pages 253–261, 1993.Google Scholar
  5. 5.
    A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth. Learnability and the Vapnik-Chervonenkis dimension. Journal of the ACM, 36(4):929–965, 1989.Google Scholar
  6. 6.
    N. Bshouty, Z. Chen, and S. Homer. On Learning Discretized Geometric Concepts. Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pages 54–63, 1994.Google Scholar
  7. 7.
    Zhixiang Chen. Learning Unions of Two Rectangles in the Plane with Equivalence Queries. Proceedings of the 6th Annual Workshop on Computational Learning Theory, pages 243–252, 1993.Google Scholar
  8. 8.
    Zhixiang Chen and Steven Homer. Learning Unions of Rectangles with Queries. Unpublished Manuscript, July 1993.Google Scholar
  9. 9.
    Zhixiang Chen and Wolfgang Maass. On-line Learning of Rectangles. Proceedings of the 5th Annual Workshop on Computational Learning Theory, pages 87–92, 1992.Google Scholar
  10. 10.
    Sally Floyd. On Space-bounded Learning and the Vapnik-Chervonenkis Dimension. Technical Report 89-061, ICSI, Berkely, 1989.Google Scholar
  11. 11.
    Sally Floyd and Manfred Warmuth. Sample Compression, Learnability, and the Vapnil-Chervonenkis dimension. Technical Report UCSC-CRL-93-13, University of California, Santa Cruz, March 1993.Google Scholar
  12. 12.
    P. Goldberg, S. Goldman, and D. Mathias. Learning Unions of Boxes with Membership and Equivalence Queries. Proceedings of the 7th Annual Workshop on Computational Learning Theory, pages 198–207, 1994.Google Scholar
  13. 13.
    Wolfgang Maass and György Turan. Algorithms and lower bounds for on-line learning of geometrical concepts. Technical Report 316, Institutes for Information Processing Graz, October 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Foued Ameur
    • 1
  1. 1.Heinz Nixdorf Institute and Dept. of Mathematics & Computer ScienceUniversity of PaderbornPaderbornGermany

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