Abstract
We consider the on-line learnability from equivalence queries only of axis-parallel rectangles over the discrete grid {1,..., n}d (BOX d n ). 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 d n due to Chen and Maass [9]. Their algorithm has learning complexity O(d 2 log n) requires space Θ(d 2logn) and time Ω(log(d 2log n)) for each learning step. We present an on-line learning algorithm for BOX d n with the same learning complexity, time complexity O(d 3log n) which is 2d-space-bounded.
Supported in part by the ESPRIT Basic Research Action No 7141 (ALCOM II) and by the DFG grant Di 412/2-1.
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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.
Foued Ameur. Space-bounded Identification of Halfplanes in the discrete Grid. AAAI-94 Fall Symposium Series, pages 5–8, 1994.
Dana Angluin. Queries and Concept Learning. Machine Learning, 2:319–342, 1988.
Peter Auer. On-line Learning of Rectangles in Noisy Environments. Proceedings of the 6th Annual Workshop on Computational Learning Theory, pages 253–261, 1993.
A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth. Learnability and the Vapnik-Chervonenkis dimension. Journal of the ACM, 36(4):929–965, 1989.
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.
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.
Zhixiang Chen and Steven Homer. Learning Unions of Rectangles with Queries. Unpublished Manuscript, July 1993.
Zhixiang Chen and Wolfgang Maass. On-line Learning of Rectangles. Proceedings of the 5th Annual Workshop on Computational Learning Theory, pages 87–92, 1992.
Sally Floyd. On Space-bounded Learning and the Vapnik-Chervonenkis Dimension. Technical Report 89-061, ICSI, Berkely, 1989.
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.
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.
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.
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© 1995 Springer-Verlag Berlin Heidelberg
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Ameur, F. (1995). A space-bounded learning algorithm for axis-parallel rectangles. In: Vitányi, P. (eds) Computational Learning Theory. EuroCOLT 1995. Lecture Notes in Computer Science, vol 904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59119-2_187
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DOI: https://doi.org/10.1007/3-540-59119-2_187
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