Bayesian wavelet networks for nonparametric regression

IEEE Transactions on Neural Networks

Volumn 11, Issue 1, 2000, Pages 27-35

  Holmes, Chris C ^a   Mallick, Bani K ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS; PROBABILITY DISTRIBUTIONS; REGRESSION ANALYSIS;

BAYESIAN WAVELET NETWORKS; MARKOV CHAIN MONTE CARLO (MCMC) ALGORITHMS; RADIAL BASIS FUNCTION (RBF) NETWORKS;

NEURAL NETWORKS;

EID: 0033640675     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.822507     Document Type: Article

References (27)

1. J. Bernardo and A. Smith, Bayesian Theory. New York: Wiley, 1994.
2. C. Bishop, Neural Networks for Pattern Recognition. Oxford, U.K.: Oxford Univ. Press, 1995.
3. L. Cao, Y. Hong, H. Fang, and G. He, "Predicting chaotic time series with wavelet networks," Phys. D, vol. 85, pp. 225-238, 1995.
4. M. Casdagli, "Nonlinear prediction of chaotic time series," Phys. D, vol. 35, pp. 335-356, 1989.
5. C. K. Chui, Wavelets: A Tutorial in Theory and Applications, C. K. Chui, Ed. New York: Academic, 1992.
6. D. Denison, B. Mallick, and A. F. M. Smith, Bayesian M.A.R.S., vol. 8, pp. 37-346, 1998.
7. D. Draper, "Assessment and propagation of model uncertainty (with discussion)," J. Roy. Statist. Soc. B, vol. 57, pp. 45-98, 1995.
8. J. D. Falmer and J. J. Sidorowich, "Predicting chaotic time series," Phys. Rev. Lett., vol. 59, no. 8, pp. 845-848, 1987.
9. A. Gelman, G. O. Roberts, and W. R. Gilks, "Efficient metropolis jumping rules," in Bayesian Statistics 5, J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Eds. Oxford, U.K.: Oxford Univ. Press, 1996.
10. P. J. Green, "Reversible jump Markov chain Monto Carlo computation and Bayesian model determination," Biometrika, vol. 82, pp. 711-732, 1995.
11. T. J. Hastie and R. J. Tibshirani, Generalized Additive Models. London, U.K.: Chapman andHall, 1990.
12. W. K. Hastings, "Monte Carlo sampling methods using Markov chains and their applications," Biometrika, vol. 57, pp. 97-109, 1970.
13. C. Holmes and B. Mallick, Bayesian Radial Basis Functions of Variable Dimension, vol. 10, pp. 1217-1233, 1998.
14. J. Hwang, S. Lay, R. Maechler, D. Martin, and J. Schimert, "Regression modeling in backpropagation and projection pursuit learning," IEEE Trans. Neural Networks, vol. 5, no. 3, pp. 342-353, 1994.
15. R. E. Kass and A. E. Raftery, "Bayes factors," J. Amer. Statist. Assoc., vol. 90, no. 430, pp. 773-795, 1995.
16. T. Kugarajah and Q. Zhang, "Multidimensional wavelet frames," IEEE Trans. Neural Networks, vol. 6, pp. 1552-1556, 1995.
17. "Tech Rep. LA-UR 87-2662," Los Alamos Nat. Lab., Los Alamos, NM, 1987.
18. B. Lillekjendlie, D. Kugiumtzis, and N. Christophersen, "Chaotic time series Part II. System identication and prediction," Modeling, Identification, Contr., vol. 15, no. 4, pp. 225-243, 1994.
19. D. MacKay, "Bayesian interpolation," Neural Comput., vol. 4, pp. 415-447, 1992a.
20. _, "A practical Bayesian framework forbackpropagation networks," Neural Comput., vol. 4, pp. 448-472, 1992b.
21. M. C. Mackey and L. Glass, "Oscillations and chaos in physiological control systems," Science, vol. 287, 1977.
22. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Pys., vol. 21, pp. 1087-1091, 1953.
23. A. F. M. Smith and G. O. Roberts, "Bayesian computation via Gibbs sampler and related Markov chain Monte Carlo methods," J. Roy. Statist. Soc. B, vol. 55, pp. 2-24, 1993.
24. F. Tarkens, "Detecting strange attractors in turbulence," in Dynamical Systems and Turbulence, Lecture Notes in Math. 898. Berlin, Germany: Springer-Verlag, 1981, pp. 366-381.
25. L. Tierney, "Markov chains for exploring posterior distributions," Ann. Statist., vol. 22, pp. 1701-1762, 1994.
26. Q. Zhang, "Using wavelet network in nonparametric estimation," IEEE Trans. Neural Networks, vol. 8, no. 2, pp. 227-236, 1997.
27. Q. Zhang and A. Benveniste, "Wavelet networks," IEEE Trans. Neural Networks, vol. 3, pp. 889-898, 1992.