Bounds on the number of examples needed for learning functions

SIAM Journal on Computing

Volumn 26, Issue 3, 1997, Pages 751-763

  Simon, Hans Ulrich ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Function learning; Sample complexity

Indexed keywords

EID: 0009625881     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539793259185     Document Type: Article

References (14)

1. M. ANTHONY, N. BIGGS, AND J. SHAWE-TAYLOR, The learnability of formal concepts, in Proc. 3rd Annual Workshop on Computational Learning Theory, Morgan Kaufmann, San Mateo, CA, 1990, pp. 246-258.
2. M. ANTHONY AND J. SHAWE-TAYLOR, Valid generalization of functions from close approximation on a sample, in Proc. European Conference on Computational Learning Theory, 1993, Oxford University Press, 1994, pp. 95-109.
3. A. BLUMER, A. EHRENFEUCHT, D. HAUSSLER, AND M. K. WARMUTH, Learnability and the Vapnik-Chervonenkis dimension, J. Assoc. Comput. Mach., 36 (1989), pp. 929-965.
4. A. EHRENFEUCHT, D. HAUSSLER, M. KEARNS, AND L. VALIANT, A general lower bound on the number of examples needed for learning, Inform. and Comput., 82 (1989), pp. 247-261.
5. D. HAUSSLER, Generalizing the pac model: Sample size bounds from metric-dimension based uniform convergence results, in Proc. 30th Annual Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1989, pp. 40-46.
6. M. J. KEARNS AND R. E. SCHAPIRE, Efficient distribution-free learning of probabilistic concepts, in Proc. 31st Annual Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 382-392; full version, J. Comput. System Sci., 48 (1994), pp. 464-497.
7. M. J. KEARNS AND R. E. SCHAPIRE, Efficient distribution-free learning of probabilistic concepts, in Proc. 31st Annual Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 382-392; full version, J. Comput. System Sci., 48 (1994), pp. 464-497.
8. D. KIMBER AND P. M. LONG, The learning complexity of smooth functions of a single variable, in Proc. 5th Annual Workshop on Computational Learning Theory, ACM, New York, 1992, pp. 153-160.
9. D. E. KNUTH, The Art of Computer Programming: Fundamental Algorithms, Vol. 1, 2nd ed., Addison-Wesley, Reading, MA, 1973.
10. B. K. NATARAJAN, On learning sets and functions, Mach. Learning, 4 (1989), pp. 67-97.
11. J. SHAWE-TAYLOR, M. ANTHONY, AND N. BIGGS, Bounding sample size with the Vapnik-Chervonenkis dimension, Discrete Appl. Math., 41 (1993), pp. 65-73.
12. H. U. SIMON, General bounds on the number of examples needed for learning probabilistic concepts, in Proc. 6th Annual Workshop on Computational Learning Theory, ACM, New York, 1993, pp. 402-412; J. Comput. System Sci., 52 (1996), pp. 239-255.
13. H. U. SIMON, General bounds on the number of examples needed for learning probabilistic concepts, in Proc. 6th Annual Workshop on Computational Learning Theory, ACM, New York, 1993, pp. 402-412; J. Comput. System Sci., 52 (1996), pp. 239-255.
14. L. G. VALIANT, A theory of the learnable, Comm. Assoc. Comput. Mach., 27 (1984), pp. 1134-1142.