Learning an Intersection of a Constant Number of Halfspaces over a Uniform Distribution

Journal of Computer and System Sciences

Volumn 54, Issue 2, 1997, Pages 371-380

  Blum, Avrim L ^a   Kannan, Ravindran ^b  

^a Carnegie Mellon University   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; POLYNOMIALS; VECTORS;

BOUNDING HYPERPLANES; UNIFORM DISTRIBUTION;

ALGORITHMS;

EID: 0031121882     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1997.1475     Document Type: Article

References (12)

1. E. B. Baum, Polynomial time algorithms for learning neural nets, in "Proceedings, Third Annual Workshop on Computational Learning Theory," pp. 258-272, Morgan Kaufmann, San Mateo, CA, 1990.
2. E. B. Baum, On learning a union of half spaces, J. Complexity 6, No. 1 (1990), 67-101.
3. M. Berger, "Geometry," Springer-Verlag, New York/Berlin, 1987.
4. A. Blum and R. Rivest, Training a 3-node neural network is NP-Complete, Neural Netorks 5 (1992), 117-127.
5. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth, Learnability and the Vapnik-Chervonenkis dimension, J. Assoc. Comput. Mach. 36, No. 4 (1989), 929-965.
6. M. Kearns, Efficient noise-tolerant from statistical queries, in "Proceedings, Twenty-Fifth Annual ACM Symposium on Theory of Computing, May 1993," pp. 392-401.
7. M. Kearns, M. Li, L. Pitt, and L. G. Valiant, On the learnability of Boolean formulae, in "Proceedings, Nineteenth Annual ACM Symposium on Theory of Computing, May 1987," pp. 285-295.
8. P. M. Long and M. K. Warmuth, Composite geometric concepts and polynomial predictability, in "Proceedings, Third Annual Workshop on Computational Learning Theory," pp. 273-287, Morgan Kaufmann, San Mateo, CA, 1990.
9. L. Lovász and M. Simonovits, The mixing rate of markov chains, an isoperimetric inequality, and computing the volume, in "Proceedings 31st Annual Symposium on Foundations of Computer Science, St. Louis, October, 1990," Vol. I, pp. 346-354.
10. N. Megiddo, "On the Complexity of Polyhedral Separability," Technical Report RJ 5252, IBM Almaden Research Center, August 1986.
11. D. F. Morrison, "Multivariate Statistical Methods," 3rd ed., McGraw-Hill, New York, 1990.
12. L. G. Valiant, A theory of the learnable, Comm. ACM 27, No. 11 (1984), 1134-1142.