On the sample complexity for neural trees

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1501, Issue , 1998, Pages 375-384

  Schmitt, Michael ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX NETWORKS; FEEDFORWARD NEURAL NETWORKS; FORESTRY; LEARNING ALGORITHMS;

LINEAR FUNCTIONS; LINEAR GATES; NEURAL TREES; SAMPLE COMPLEXITY; THRESHOLD TREES; UPPER BOUND; VC DIMENSION;

TREES (MATHEMATICS);

EID: 84961363381     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-49730-7_26     Document Type: Conference Paper

References (22)

1. D. Angluin, L. Hellerstein, and M. Karpinski. Learning read-once formulas with queries. Journal of the Association for Computing Machinery, 40:185-210, 1993.
2. M. Anthony and N. Biggs. Computational Learning Theory. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, 1992.
3. E. B. Baum and D. Haussler. What size net gives valid generalization? Neural Computation, 1:151-160, 1989.
4. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth. Learnability and the Vapnik-Chervonenkis dimension. Journal of the Association for Computing Machinery, 36:929-965, 1989.
5. T. M. Cover. Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Transactions on Electronic Computers, 14:326-334, 1965.
6. T. M. Cover. Capacity problems for linear machines. In L. N. Kanal, editor, Pattern Recognition, pages 283-289, Thompson Book Co., Washington, 1968.
7. P. W. Goldberg and M. R. Jerrum. Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers. Machine Learning, 18:131-148, 1995.
8. M. Golea, M. Marchand, and T. R. Hancock. On learning μ-Perceptron networks with binary weights. In S. J. Hanson, J. D. Cowan, and C. L. Giles, editors, Advances in Neural Information Processing Systems 5, pages 591-598. Morgan Kaufmann, San Mateo, CA, 1993.
9. M. Golea, M. Marchand, and T. R. Hancock. On learning μ-Perceptron networks on the uniform distribution. Neural Networks, 9:67-82, 1996.
10. T. R. Hancock, M. Golea, and M. Marchand. Learning nonoverlapping Perceptron networks from examples and membership queries. Machine Learning, 16:161-183, 1994.
11. D. Haussler. Decision theoretic generalizations of the PAC model for neural net and other learning applications. Information and Computation, 100:78-150, 1992.
12. M. Karpinski and A. Macintyre. Polynomial bounds for VC dimension of sigmoidal and general pfaffian neural networks. Journal of Computer and System Sciences, 54:169-176, 1997.
13. P. Koiran and E. D. Sontag. Neural networks with quadratic VC dimension. Journal of Computer and System Sciences, 54:190-198, 1997.
14. N. Littlestone. Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm. Machine Learning, 2:285-318, 1988.
15. W. Maass. Neural nets with superlinear VC-dimension. Neural Computation, 6:877-884, 1994.
16. W. Maass. Vapnik-Chervonenkis dimension of neural nets. In M. A. Arbib, editor, The Handbook of Brain Theory and Neural Networks, pages 1000-1003. MIT Press, Cambridge, Mass., 1995.
17. W. Maass, G. Schnitger, and E. D. Sontag. A comparison of the computational power of sigmoid and Boolean threshold circuits. In V. Roychowdhury, K.-Y. Siu, and A. Orlitsky, editors, Theoretical Advances in Neural Computation and Learning, pages 127-151. Kluwer, Boston, 1994.
18. W. Maass and G. Turan. Lower bound methods and separation results for on-line learning models. Machine Learning, 9:107-145, 1992.
19. A. Sakurai. Tighter bounds of the VC-dimension of three-layer networks. In Proceedings of the World Congress on Neural Networks WCNN'93, volume 3, pages 540-543, 1993.
20. L. Schlafli. Theorie der vielfachen Kontinuitat.Zürcher & Furrer, Zürich, 1901. Reprinted in: L. Schlüfli, Gesammelte Mathematische Abhandlungen, Band I, Birkhüauser, Basel, 1950.
21. J. Shawe-Taylor. Sample sizes for threshold networks with equivalences. Information and Computation, 118:65-72, 1995.
22. L. G. Valiant. A theory of the learnable. Communications of the ACM, 27:11341142, 1984.