Abstract
A new research frontier in AI and data mining seeks to develop methods to automatically discover relevant variables among many irrelevant ones. In this paper, we present four algorithms that output such crucial variables in PAC model with membership queries. The first algorithm executes the task under any unknown distribution by measuring the distance between virtual and real targets. The second algorithm exhausts virtual version space under an arbitrary distribution. The third algorithm exhausts universal set under the uniform distribution. The fourth algorithm measures influence of variables under the uniform distribution. Knowing the number r of relevant variables, the first algorithm runs in almost linear time for r. The second and the third ones use less membership queries than the first one, but runs in time exponential for r. The fourth one enumerates highly influential variables in quadratic time for r.
Author supported in part by the EC through the Esprit Program EU BRA program under project 20244 (ALCOM-IT) and the EC Working Group EP27150 (NeuroColt II) and by the spanish DGES PB95-0787 (Koala).
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, 1987.
M. Ben-Or and N. Linial. Collective coin flipping. Advances in Computing Research, 5, 1989.
A. Blum, M. Furst, M.l. Kearns, and R. J. Lipton. Cryptographic primitives based on hard learning problems. In Proc. CRYPTO 93, pages 278–291, 1994. LNCS 773.
A. Blum, L. Hellerstein, and N. Littlestone. Learning in the presence of finitely or infinitely many irrelevant attributes. Journal of Computer and System Sciences, 50(1):32–40, 1995.
A.L. Blum and P. Langrey. Selection of relevant features and examples. Machine Learning. to be appeared.
B. Bollobas. Combinatorics. Cambridge Univ. Press, Cambridge, 1986.
P. Damaschke. Adaptive versus nonadaptive attribute-efficient learning. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC-98), pages 590–596, 1998
A. Dhagat and L. Hellerstein. PAC learning with irrelevant attributes. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pages 64–74, 1994.
D. Haussler. Quantifying inductive bias: AI learning algorithms and Valiant’s model. Artificial Intelligence, 36(2):177–221, 1988.
R. Uehara, K. Tsuchida, and I. Wegener. Optimal attribute-efficient learning of disjunction, parity and threshold functions. In Proceedings of the 3rd European Conference on Computational Learning Theory, volume 1208 of LNAI, pages 171–184, 1997.
L. G. Valiant. A theory of the learnable. Communications of the ACM, 27(11):1134–1142, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Guijarro, D., Tarui, J., Tsukiji, T. (1999). Finding Relevant Variables in PAC Model with Membership Queries. In: Watanabe, O., Yokomori, T. (eds) Algorithmic Learning Theory. ALT 1999. Lecture Notes in Computer Science(), vol 1720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46769-6_26
Download citation
DOI: https://doi.org/10.1007/3-540-46769-6_26
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66748-3
Online ISBN: 978-3-540-46769-4
eBook Packages: Springer Book Archive