Abstract
We consider the exact learning in the query model. We deal with all types of queries introduced by Angluin: membership, equivalence, superset, subset, disjointness and exhaustiveness queries, and their weak (or restricted) versions where no counterexample is returned. For each of all possible combinations of these queries, we uniformly give complete characterizations of boolean concept classes that are learnable using a polynomial number of polynomial sized queries. Our characterizations show the equivalence between the learnability of a concept class C using queries and the existence of a good query for any subset H of C which is guaranteed to reject a certain fraction of candidate concepts in H regardless of the answer. As a special case for equivalence queries alone, our characterizations directly correspond to the lack of the approximate fingerprint property, which is known to be a sufficient and necessary condition for the learnability using equivalence queries
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Angluin. Queries and concept learning. Machine Learning, 2:319–342, 1988.
D. Angluin. Negative results for equivarence queries. Machine Learning, 5:121–150, 1990.
N. Bshouty, R. Cleve, R. Gavalda, S. Kannan, and C. Tamon. Oracles and queries that sufficient for exact learning. Journal of Computer and System Sciences, 52:421–433, 1996.
R. Gavaldà . On the power of equivarence queries. In Proceedings of the 1st European Conference on Computational Learning Theory, pages 193–203, 1993.
S. Goldman and M. Kearns. On the complexity of teaching. Journal of Computer and System Sciences, 50:20–31, 1995.
T. Hegedüs. Generalized teaching dimensions and the query complexity of learning. In Proceedings of the 8th Annual Conference on Computational Learning Theory, pages 108–117, 1995.
L. Hellerstein, K. Pillaipakkamnatt, V. Raghavan, and D. Wilkins. How many queries are needed to learn? Journal of the ACM, 43(5), 1996.
J. Köbler and W. Lindner. Oracles in Σ 2 p are sufficient for exact learning. In Proceedings of 8th Workshop on Algorithmic Learning Theory, pages 277–290. Springer-Verlag, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hayashi, Y., Matsumoto, S., Shinohara, A., Takeda, M. (1998). Uniform Characterizations of Polynomial-Query Learnabilities. In: Arikawa, S., Motoda, H. (eds) Discovey Science. DS 1998. Lecture Notes in Computer Science(), vol 1532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49292-5_8
Download citation
DOI: https://doi.org/10.1007/3-540-49292-5_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65390-5
Online ISBN: 978-3-540-49292-4
eBook Packages: Springer Book Archive