Fat-shattering and the learnability of real-valued functions

Journal of Computer and System Sciences

Volumn 52, Issue 3, 1996, Pages 434-452

  Bartlett, Peter L ^a   Long, Philip M ^b   Williamson, Robert C ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

FAT SHATTERING FUNCTION; LEARNABILITY; REAL VALUED FUNCTIONS; VAPNIK-CHERVONENKIS DIMENSION;

COMPUTATION THEORY; CONSTRAINT THEORY; FUNCTIONS; LEARNING ALGORITHMS; MATHEMATICAL MODELS; PERFORMANCE; POLYNOMIALS; PROBABILITY; RANDOM PROCESSES; SPURIOUS SIGNAL NOISE;

LEARNING SYSTEMS;

EID: 0030165580     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1996.0033     Document Type: Article

References (27)

1. N. Alon, S. Ben-David, N. Cesa-Bianchi, and D. Haussler, Scale-sensitive dimensions, uniform convergence, and leamability, in "Symposium on Foundations of Computer Science, 1993."
2. D. Angluin and L. G. Valiant, Fast probabilistic algorithms for Hamiltonian circuits and matchings, J. Comput. System Sci. 18 (1979), 155-193.
3. M. Anthony and P. L. Bartlett, Function learning from interpolation, in "Computational Learning Theory: EUROCOLT '95, 1995."
4. M. Anthony, P. L. Bartlett, Y. Ishai, and J. Shawe-Taylor, Valid generalisation from approximate interpolation, Combinatorics, Probability and Computing, to appear.
5. M. Anthony and J. Shawe-Taylor, Valid generalization from approximate interpolation, in "Computational Learning Theory: EUROCOLT '93, 1993."
6. P. Auer, P. M. Long, W. Maass, and G. J. Woeginger, On the complexity of function learning, in "Proceedings, Sixth Annual ACM Conference on Computational Learning Theory, 1993."
7. P. Auer and P. M. Long, Simulating access to hidden information while learning, in "Proceedings, 26th Annual ACM Symposium on the Theory of Computation, 1994."
8. P. L. Bartlett, Learning with a slowly changing distribution, in "Proceedings, Fifth Annual ACM Workshop on Computational Learning Theory, New York, 1992."
9. P. L. Bartlett and P. M. Long, More theorems about scale-sensitive dimensions and learning, in "Proceedings, Eighth Annual ACM Conference on Computational Learning Theory, 1995."
10. P. L. Bartlett, P. M. Long, and R. C. Williamson, Fat-shattering and the learnability of real-valued functions (extended abstract), in "Proceedings, Seventh Annual ACM Conference on Computational Learning Theory, 1994."
11. S. Ben-David, N. Cesa-Bianchi, D. Haussler, and P. Long, Characterizations of learnability for classes of {0,...,n}-valued functions, J. Comput. System Sci. 50 (1995), 74-86.
12. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth, Learnability and the Vapnik-Chervonenkis dimension, J. Assoc. Comput. Mach. 36 (1989), 929-965.
13. S. van de Geer, Regression analysis and empirical processes, in "Centrum voor Wiskunde en Informatica, Amsterdam, 1988."
14. L. Gurvits and P. Koiran, Approximation and learning of convex superpositions, in "Computational Learning Theory: EUROCOLT '95, 1995."
15. D. Haussler, Decision theoretic generalizations of the PAC model for neural net and other learning applications, Inform. and Comput. 100 (1992), 78-150.
16. M. J. Kearns and R. E. Schapire, Efficient distribution-free learning of probabilistic concepts (extended abstract), in "Proceedings, 31st Annual Symposium on the Foundations of Computer Science, 1990."
17. M. J. Kearns, R. E. Schapire, and L. M. Sellie, Toward efficient agnostic learning, Mach. Learning 17 (1994), 115.
18. N. Merhav and M. Feder, Universal schemes for sequential decision from individual data sequences, IEEE Trans. Inform. Theory 39 (1993), 1280-1292.
19. B. K. Natarajan, On learning sets and functions, Mach. Learning 4 (1989), 67-97.
20. B. K. Natarajan, Occam's razor for functions, in "Proceedings, Sixth Annual ACM Conference on Computational Learning Theory, 1993."
21. J. K. Patel and C. B. Read, "The Big Book of Facts about the Normal Distribution," Dekker, New York, 1982.
22. D. Pollard, "Convergence of Stochastic Processes," Springer-Verlag, New York, 1984.
23. H. L. Royden, "Real Analysis," Macmillan Co., New York, 1988.
24. J. Shawe-Taylor, M. Anthony, and N. Biggs, Bounding sample size with the Vapnik-Chervonenkis dimension, Discrete Appl. Math. 42 (1993), 65-73.
25. H. U. Simon, Bounds on the number of examples needed for learning functions, FB Informatik, LS II, Forschungsbericht Nr. 501, Universität Dortmund, 1993.
26. L. G. Valiant, A theory of the learnable, Comm. ACM 27 (1984), 1134-1143.
27. V. N. Vapnik and A. Y. Chervonenkis, On the uniform convergence of relative frequencies of events to their probabilities, Theory Probab. Appl. 16 (1971), 264-280.