On Restricted-Focus-of-Attention learnability of boolean functions

Machine Learning

Volumn 30, Issue 1, 1998, Pages 89-123

  Birkendorf, Andreas ^a   Dichterman, Eli ^b,c   Jackson, Jeffrey ^d   Klasner, Norbert ^a   Simon, Hans Ulrich ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^c UNIVERSITY OF LONDON   (United Kingdom)

^d DUQUESNE UNIVERSITY   (United States)

Author keywords

Boolean Function Classes; Decision Lists; Fourier Transform; Learning Algorithms; PAC Learning; Restricted Focus of Attention; Threshold of Parities

Indexed keywords

BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; DECISION THEORY; FOURIER TRANSFORMS; INFORMATION THEORY; LEARNING ALGORITHMS; MATHEMATICAL MODELS;

DECISION LISTS; PAC LEARNING; RESTRICTED FOCUS OF ATTENTION MODEL;

LEARNING SYSTEMS;

EID: 0031679046     PISSN: 08856125     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007458528570     Document Type: Article

References (30)

1. Aho, A. V., Hopcroft, J. E., and Ullman, J. D. (1974). The Design and Analysis of Computer Algorithms. Addison-Wesley.
2. Angluin, D. and Valiant, L. G. (1979). Fast probabilistic algorithms for hamiltonian circuits and matchings. Journal of Computer Systems and Sciences, 18:155-193.
3. Ben-David, S. and Dichterman, E. (1993). Learning with restricted focus of attention. In Proceedings of the 6th Annual Conference on Computational Learning Theory, pages 287-296. ACM Press, New York, NY.
4. Ben-David, S. and Dichterman, E. (1994). Learnability with restricted focus of attention guarantees noise-tolerance. In 5th International Workshop on Algorithmic Learning Theory, ALT'94, pages 248-259.
5. Ben-David, S. and Dichterman, E. (1997). Learning with restricted focus of attention. Technical Report LSE-CDAM-97-01, London School of Economics.
6. Blum, A. and Chalasani, P. (1992). Learning switching concepts. In Proceedings of the 5th Annual Workshop on Computational Learning Theory, pages 231-242.
7. Blum, A., Furst, M., Jackson, J. C., Kearns, M., Mansour, Y., and Rudich, S. (1994). Weakly learning DNF and characterizing statistical query learning using fourier analysis. In Proceedings of the 26th Annual ACM Symposium on Theory of Computing, pages 253-262.
8. Blumer, A., Ehrenfeucht, A., Haussler, D., and Warmuth, M. K. (1989). Learnability and the Vapnik-Chervonenkis dimension. JACM, 36(4):929-965.
9. Bruck, J. (1990). Harmonic analysis of polynomial threshold functions. SIAM Journal of Discrete Mathematics, 3(2):168-177.
10. Chow, C. (1961). On the characterization of threshold functions. In Proc. Symp. on Switching Circuit Theory and Logical Design, pages 34-38.
11. Decatur, S. E. and Gennaro, R. (1995). On learning from noisy and incomplete examples. In Proceedings of the 8th Annual Conference on Computational Learning Theory, pages 353-360.
12. Domingo, C. Private communication.
13. Ehrenfeucht, A., Haussler, D., Kearns, M., and Valiant, L. G. (1989). A general lower bound on the number of examples needed for learning. Information and Computation, 82:247-261.
14. First appeared in Proceedings of the 1st Annual Workshop on Computational Learning Theory.
15. Freund, Y. (1990). Boosting a weak learning algorithm by majority. In Proceedings of the 3rd Annual Workshop on Computational Learning Theory, pages 202-216. Morgan Kaufmann, San Mateo, CA.
16. Freund, Y. (1993). Data Filtering and Distribution Modeling Algorithms for Machine Learning. PhD thesis, University of California, Santa Cruz.
17. Goldman, S. A. and Sloan, R. H. (1995). Can PAC learning algorithms tolerate random attribute noise? Algorithmica, 14:70-84.
18. Jackson, J. C. (1994). An efficient membership-query algorithm for learning DNF with respect to the uniform distribution. In Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, pages 42-53.
19. Jackson, J. C. (1995). The Harmonic Sieve: A Novel Application of Fourier Analysis to Machine Learning Theory and Practice. PhD thesis, Carnegie Mellon University. Available as technical report CMU-CS-95-183.
20. Kearns, M. J. (1993). Efficient noise-tolerant learning from statistical queries. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 392-401.
21. Kearns, M. J. and Li, M. (1993). Learning in the presence of malicious errors. SIAM J. Comput., 22:807-837.
22. Kearns, M. J. and Schapire, R. E. (1990). Efficient distribution-free learning of probabilistic concepts. In Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science, pages 382-391.
23. Kearns, M. J., Schapire, R. E., and Sellie, L. M. (1992). Towards efficient agnostic learning. In Proceedings of the 5th Annual Workshop on Computational Learning Theory, pages 341-352.
24. Linial, N., Mansour, Y., and Nisan, N. (1993). Constant depth circuits, Fourier transform, and learnability. Journal of the ACM, 40(3):607-620.
25. Earlier version appeared in Proceedings of the 30th Annual Symposium on Foundations of Computer Science, pages 574-579, 1989.
26. Rivest, R. L. (1987). Learning decision lists. Machine Learning, 2:229-246.
27. Schapire, R. E. (1990). The strength of weak learnability. Machine Learning, 5:197-227.
28. Simon, H. U. (1995). Learning decision lists and trees with equivalence-queries. In Proceedings of the 2nd European Conference on Computational Learning Theory, pages 322-336.
29. Valiant, L. G. (1984). A theory of the learnable. CACM, 27(11):1134-1142.
30. Vapnik, V. N. and Chervonenkis, A. Y. (1971). On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its applications, XVI(2):264-280.