Abstract
This note studies the learnability of the class k-term DNF with a bounded number of negations per term. We study the case of learning with membership queries alone, and give tight upper and lower bounds on the number of negations that makes the learning task feasible. We also prove a negative result for equivalence queries. Finally, we show that a slight modification in our algorithm proves that the considered class is also learnable in the Simple PAC model, extending Li and Vitányi result for monotone k-term DNF.
Research supported by the Esprit EC program under project 7141 (ALCOM-II), the Working Group 8556 (NeuroColt), and the Spanish DGICYT (project PB92-0709).
Supported by FP93 13717942 grant from the Spanish Government.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
D. Angluin. “Learning k-term DNF formulas using queries and counterexamples”. Technical Report YALEU/DCS/RR-559, Yale University, August 1987.
D. Angluin. “Learning regular sets from queries and counterexamples”. Information and Computation, 75:87–106, November 1987.
D. Angluin. “Queries and concept learning”. Machine Learning, 2(4):319–342, 1988.
Ulf Berggren. “Linear Time Deterministic Learning of k-term DNF” In Proc. 6th Annu. Workshop on Comput. Learning Theory, pages 37–40. ACM Press, New York, NY, 1993.
N. Bshouty. “Simple Learning Algorithms Using Divide and Conquer”. In Proc. of 8th Annu. ACM Workshop on Comput. Learning Theory, pages 447–453, 1995.
N. Bshouty, R. Cleve, R. Gavaldà, S. Kannan, and C. Tamon. “Oracles and queries that are sufficient for exact learning”. Journal of Computer and System Sciences, 52, pp. 421–433, 1996.
N. Bshouty, S. Goldman, T. Hancock, and S. Matar. “Asking queries to minimize errors”. In Proc. 6th Annu. Workshop on Comput. Learning Theory, pages 41–50. ACM Press, New York, NY, 1993.
M. Li and P. Vitányi. “Learning simple concepts under simple distributions”. SIAM Journal of Computing 20, pages 911–935, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Castro, J., Guijarro, D., Lavín, V. (1997). Learning nearly monotone k-term DNF. In: Ben-David, S. (eds) Computational Learning Theory. EuroCOLT 1997. Lecture Notes in Computer Science, vol 1208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62685-9_14
Download citation
DOI: https://doi.org/10.1007/3-540-62685-9_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62685-5
Online ISBN: 978-3-540-68431-2
eBook Packages: Springer Book Archive