Statistical mechanics of ensemble learning

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 1, 1997, Pages 811-825

  Krogh, Anders ^a   Sollich, Peter ^b  

^a NORDITA   (Denmark)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039240492     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.811     Document Type: Article

References (32)

1. J. Hertz, A. Krogh, and R G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Redwood City, CA, 1991).
2. T. L. H. Watkin, A. Rau and M. Biehl, Rev. Mod. Phys.65, 499 (1993).
3. C. W. J. Granger, J. Forecast.8, 167 (1989).
4. D H. Wolpert, Neural Networks5, 241 (1992).
5. L. Breimann, University of California at Berkeley Technical Report No. 367, 1992 (unpublished).
6. L K. Hansen and P. Salamon, IEEE Trans. Pattern Anal. Mach. Intell.12, 993 (1990).
7. M P. Perrone and L N. Cooper, in Neural Networks for Speech and Image Processing, edited by R. J. Mammone (Chapman-Hall, London, 1993).
8. S. Hashem, IEEE Trans. Neural Networks6, 792 (1995).
9. A. Krogh and J. Vedelsby, in Advances in Neural Information Processing Systems 7, edited by G. Tesauro, D. S. Touretzky, and T. K. Leen (MIT Press, Cambridge, MA, 1995), pp. 231–238.
10. R. Jacobs, M. Jordan, S. Nowlan and G. Hinton, Neural Comput.3, 79 (1991).
11. R E. Schapire, Mach. Learn.5, 197 (1990).
12. Y. Freund, Inf. Comput.121, 256 (1995).
13. R. Meir, in Advances in Neural Information Processing Systems 7, (Ref. [9]), pp. 295–302.
14. P. Sollich and A. Krogh, in Advances in Neural Information Processing Systems 8, edited by D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo (MIT Press, Cambridge, MA, 1996), pp. 190–196.
15. S. Geman, E. Bienenstock and R. Doursat, Neural Comput.4, 1 (1992).
16. D. J. C. MacKay, Neural Comput.4, 448 (1992).
17. W L. Buntine and A S. Weigend, Compl. Syst.5, 603 (1991).
18. A. Bruce and D. Saad, J. Phys. A27, 3355 (1994).
19. H S. Seung, H. Sompolinsky, and N. Tishby, Phys. Rev. A45, 6056 (1992).
20. The factor 2 in the Gibbs distribution is introduced merely in order to eliminate cumbersome numerical factors in later results.
21. P. Sollich, J. Phys. A27, 7771 (1994).
22. A. Krogh and J A. Hertz, J. Phys. A25, 1135 (1992).
23. J A. Hertz, A. Krogh and G I. Thorbergsson, J. Phys. A22, 2133 (1989).
24. P. Sollich, J. Phys. A28, 6125 (1995).
25. S. Bös, W. Kinzel and M. Opper, Phys. Rev. E47, 1384 (1993).
26. T. L. H. Watkin, Europhys. Lett.21, 871 (1993).
27. J. Berger, Statistical Decision Theory and Bayesian Analysis (Springer, New York, 1985).
28. J. Pilz, Bayesian Estimation and Experimental Design in Linear Regression Models, 2nd ed. (Wiley, Chichester, 1991).
29. D. J. C. MacKay, Neural Comput.4, 415 (1992).
30. A. Krogh, J. Phys. A25, 1119 (1992).
31. In fact, it suffices that the norm of M (i.e., its maximal eigenvalue) be of O(1).
32. M L. Eaton, Multivariate Statistics—A Vector Space Approach (Wiley, New York, 1983).