Weakly learning DNF and characterizing statistical query learning using fourier analysis

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn Part F129502, Issue , 1994, Pages 253-262

  Blum, Avrim ^a   Furst, Merrick ^a   Jackson, Jeffrey ^a   Kearns, Michael ^b   Mansour, Yishay ^c   Rudich, Steven ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b LUCENT TECHNOLOGIES   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

DECISION THEORY; DECISION TREES; FORESTRY; FOURIER ANALYSIS; INFORMATION THEORY; LEARNING SYSTEMS; POLYNOMIAL APPROXIMATION; POLYNOMIALS; STATISTICS; TREES (MATHEMATICS); ALGORITHMS; BOOLEAN FUNCTIONS; FOURIER TRANSFORMS; MATHEMATICAL MODELS; STATISTICAL METHODS; THEOREM PROVING;

COMPUTATIONAL LEARNING THEORY; CRYPTOGRAPHIC ASSUMPTIONS; DISJUNCTIVE NORMAL FORM; MACHINE LEARNING COMMUNITIES; PROBABLY APPROXIMATELY CORRECT; SIMPLE MODIFICATIONS; STATISTICAL QUERY MODELS; UPPER AND LOWER BOUNDS;

LEARNING ALGORITHMS; QUERY LANGUAGES;

DISJUNCTIVE NORMAL FORM EXPRESSIONS; PROBABLY APPROXIMATELY CORRECT LEARNING MODEL; STATISTICAL QUERY LEARNING;

EID: 0028062299     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/195058.195147     Document Type: Conference Paper

References (23)

1. Howard Aizenstein, Lisa Hellerstein, and Leonard Pitt. Read-Thrice DNF is hard to learn with membership andequivalence queries. In Proceedings of the 33rd Annual Symposium on Foundations of Computer Science, pages 523-532, 1992.
2. Howard Aizenstein and Leonard Pitt. Exact learning of read-Twice DNF formulas. In Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pages 170-179, 1991.
3. Howard Aizenstein and Leonard Pitt. Exact learning of read-fc disjoint DNF and not-so-disjoint DNF. In Proceedings of the Fifth Annual Workshop on Computational Learning Theory, pages 71-76, 1992.
4. Dana Angluin, Michael Frazier, and Leonard Pitt. Learning conjunctions of Horn clauses. In Proceedings of the 30th Annual Symposium on Foundations of Computer Science, pages 186-192, 1990.
5. Avrim Blum and Steven Rudich. Fast learning of k-Term DNF formulas with queries. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 382-389, 1992.
6. Anselm Blumer, Andrzej Ehrenfeucht, David Haussler, and Manfred Warumth. Learnability and the Vapnik-Chervonenkis Dimension. Journal of the ACM, 36(4):929-965, October 1989.
7. Bruck, J. Harmonic Analysis of Polynomial Threshold Functions. SIAM Journal of Discrete Mathematics, 5, pp. 168-177, 1990.
8. Nader H. Bshouty. Exact learning via the monotone theory. In Proceedings of the 34th Annual Symposium on Foundations of Computer Science, pages 302-311, 1993.
9. Merrick L. Furst, Jeffrey C. Jackson, and Sean W. Smith. Improved learning of ACO functions. In Fourth Annual Workshop on Computational Learning Theory, pages 317-325, 1991.
10. Thomas R. Hancock. Learning 2aDNF formulas and kfi decision trees. In Proceedings of the Fourth Annual Workshop on Computational Learning Theory, pages 199-209, 1991.
11. Michael J. Kearns. Efficient noise-Tolerant learning from statistical queries. In Proceedings of the Twenty- Fifth Annual ACM Symposium on Theory of Computing, pages 392-401, 1993.
12. Michael Kearns, Ming Li, Lenny Pitt and Leslie G. Valiant. On the learnability of Boolean formulae. In Proceedings of the 19th Annual ACM Symposium on Theory of Computing, pages 285-295, 1987.
13. Michael J. Kearns, Robert E. Schapire, and Linda M. Sellie. Toward efficient agnostic learning. In Fifth Annual Workshop on Computational Learning Theory, pages 341-352, 1992.
14. Roni Khardon. On using the Fourier transform to learn disjoint DNF. Unpublished manuscript, September 1993.
15. Michael Kharitonov. Cryptographic hardness of distribution-specific learning. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 372-381, 1993.
16. Eyal Kushilevitz and Yishay Mansour. Learning decision trees using the Fourier spectrum. SIAM Journal on Computing 22(6):1331-1348, December 1993. (Also in Proceedings of the Twenty Third Annual ACM Symposium on Theory of Computing, pages 455-464, 1991.).
17. Eyal Kushilevitz and Dan Roth. On learning visual concepts and DNF formulae. In Proceedings of the Sixth Annual Workshop on Computational Learning Theory, pages 317-326, 1993.
18. Nathan Linial, Yishay Mansour, and Noam Nisan. Constant depth circuits, Fourier transform, and learnability. Journal of the ACM 40 (3): 607-620, July 1993. (Also in 30th Annual Symposium on Foundations of Computer Science, pages 574-579, 1989.).
19. Richard Lipton. Personal communication.
20. Yishay Mansour. An 0 (n loglog n) learning algorithm for DNF under the uniform distribution. In Fifth Annual Workshop on Computational Learning Theory, pages 53-61, 1992.
21. Lenny Pitt and Leslie G. Valiant. Computational limitations on learning from examples. Journal of the ACM, 35(4): 965-984, October 1988.
22. J.R. Quinlan. Induction of decision trees. Machine Learning, 1(1):81-106.
23. L. G. Valiant. A theory of the learnable. Communications of the ACM, 27(11):1134-1142, November 1984.