Wavelet Network for Nonlinear Regression Using Probabilistic Framework

  • Shu-Fai Wong
  • Kwan-Yee Kenneth Wong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3174)


Regression analysis is an essential tools in most research fields such as signal processing, economic forecasting etc. In this paper, an regression algorithm using probabilistic wavelet network is proposed. As in most neural network (NN) regression methods, the proposed method can model nonlinear functions. Unlike other NN approaches, the proposed method is much robust to noisy data and thus over-fitting may not occur easily. This is because the use of wavelet representation in the hidden nodes and the probabilistic inference on the value of weights such that the assumption of smooth curve can be encoded implicitly. Experimental results show that the proposed network have higher modeling and prediction power than other common NN regression methods.


Hide Node Noisy Data Wavelet Function Mother Wavelet Probabilistic Framework 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Fox, J.: Multiple and Generalized Nonparametric Regression. Sage Publications, Thousand Oaks CA (2000)zbMATHGoogle Scholar
  2. 2.
    Stern, H.S.: Neural networks in applied statistics. Technometrics 38, 205–214 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bansal, A., Kauffmann, R., Weitz, R.: Comparing the modeling performance of regression and neural networks as data quality varies: A business value approach. Journal of Management Information Systems 10, 11–32 (1993)Google Scholar
  4. 4.
    Cybenko, G.: Approximation by superposition of a sigmoidal function. Mathematics of Control, Signals and Systems 2, 303–314 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2, 359–366 (1989)CrossRefGoogle Scholar
  6. 6.
    Park, J., Sandberg, I.W.: Universal approximation using radial-basis function networks. Neural Computation 3, 246–257 (1991)CrossRefGoogle Scholar
  7. 7.
    Donoho, D., Johnstone, I.: Ideal spatial adaption by wavelet shrinkage. Biometrika 81, 425–455 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Zhang, Q.: Using wavelet network in nonparametric estimation. IEEE Trans. Neural Networks 8, 227–236 (1997)CrossRefGoogle Scholar
  9. 9.
    MacKay, D.J.C.: Bayesian methods for backpropagation networks. In: Domany, E., van Hemmen, J.L., Schulten, K. (eds.) Models of Neural Networks III, Springer, New York (1994)Google Scholar
  10. 10.
    Ray, S., Chan, A., Mallick, B.: Bayesian wavelet shrinkage in transformation based normal models. In: ICIP 2002, I, pp. 876–879 (2002)Google Scholar
  11. 11.
    Lillekjendlie, B., Kugiumtzis, D., Christophersen, N.: Chaotic time series - part ii: System identification and prediction. Modeling, Identification and Control 15, 225–243 (1994)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Shu-Fai Wong
    • 1
  • Kwan-Yee Kenneth Wong
    • 1
  1. 1.Department of Computer Science and Information SystemsThe University of Hong KongHong Kong

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