Prediction, Learning, Uniform Convergence, and Scale-Sensitive Dimensions

Journal of Computer and System Sciences

Volumn 56, Issue 2, 1998, Pages 174-190

  Bartlett, Peter L ^a   Long, Philip M ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; GAME THEORY; MATHEMATICAL MODELS;

SCALE SENSITIVE DIMENSIONS;

LEARNING ALGORITHMS;

EID: 0032046897     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1997.1557     Document Type: Article

References (18)

1. N. Alon, S. Ben-David, N. Cesa-Bianchi, and D. Haussler, Scale-sensitive dimensions, uniform convergence, and learnability, in "Proceedings of the 1993 IEEE Symposium on Foundations of Computer Science," IEEE Press, Los Alamitos, CA, 1993.
2. M. Anthony and P. Bartlett, Function learning from interpolation, in "Computational Learning Theory: EUROCOLT'95," 1995.
3. M. Anthony, N. Biggs, and J. Shawe-Taylor, The learnability of formal concepts, in "Proceedings of the Third Annual Workshop on Computational Learning Theory," pp. 246-257, 1990.
4. P. L. Bartlett, P. M. Long, and R. C. Williamson, Fat-shattering and the learnability of real-valued functions, J. Comput. System Sci. 52 (1996), 434-452.
5. G. M. Benedek and A. Itai, Learnability with respect to fixed distributions, Theoret. Comput. Sci. 86 (1991), 377-389.
6. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth, Learnability and the Vapnik-Chervonenkis dimension, J. Assoc. Comput. Mach. 36 (1989), 929-965.
7. K. L. Buescher and P. R. Kumar, Learning stochastic functions by smooth simultaneous estimation, in "Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory," pp. 272-279, Assoc. Comput. Mach., New York, 1992.
8. A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant, A general lower bound on the number of examples needed for learning, Inform. Comput. 82 (1989), 247-261.
9. L. Gurvits and P. Koiran, Approximation and learning of convex superpositions, in "Computational Learning Theory: EUROCOLT'95," 1995.
10. D. Haussler, Decision theoretic generalizations of the PAC model for neural net and other learning applications, Inform. Comput. 100 (1992), 78-150.
11. D. Haussler, Sphere packing numbers for subsets of the boolean n-cube with bounded Vapnik-Chervonenkis dimension, J. Combin. Theory Ser. A 69 (1995), 217-232.
12. D. Haussler, M. Kearns, N. Littlestone, and M. K. Warmuth, Equivalence of models for polynomial learnability, Inform. Comput. 95 (1991), 129-161.
13. D. Haussler, N. Littlestone, and M. K. Warmuth, Predicting {0, 1}-functions on randomly drawn points, Inform. Comput. 115 (1994), 129-161.
14. M. J. Kearns and R. E. Schapire, Efficient distribution-free learning of probabilistic concepts, J. Comput. System Sci. 48 (1994), 464-497.
15. M. J. Kearns, R. E. Schapire, and L. M. Sellie, Toward efficient agnostic learning, Mach. Learning 17 (1994), 115-141.
16. B. K. Natarajan, Occam's razor for functions, in "Proceedings of the 1993 ACM Conference on Computational Learning Theory," pp. 370-376, Assoc. Comput. Mach., New York, 1993.
17. D. Pollard, "Convergence of Stochastic Processes," Springer-Verlag, New York, 1984.
18. H. U. Simon, Bounds on the number of examples needed for learning functions, in "Computational Learning Theory: EUROCOLT '93," Oxford Univ. Press, Oxford, UK, 1994.