Robust On-Line Statistical Learning

  • Enrico Capobianco
Conference paper


We describe possible ways of endowing neural networks with statistically robust properties. We especially look at learning schemes resistant to outliers by defining error criteria able to handle deviations from convenient probability distribution assumptions. It comes out to be convenient to cast neural nets in state space representations and apply both Kalman Filter and Stochastic Approximation procedures in order to suggest statistically robustified solutions for on-line learning.


Prediction Error Kalman Filter Influence Function State Space Representation Kalman Filter Algorithm 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    E. Capobianco: “A Unifying view of Stochastic Approximation, Kaiman Filter and Backpropagation”. NNSP-IEEE Proceedings, vol. V, pp 87–94, 1995.Google Scholar
  2. [2]
    F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel: Robust Statistics: the approach based on Infiuence Function. New York, US: Wiley, 1986.Google Scholar
  3. [3]
    A.C. Harvey: Forecasting, Structural Time Series Models and the Kaiman Filter. Cambridge, UK: Cambridge University Press, 1989.Google Scholar
  4. [4]
    P.J. Huber: Robust Statistics. New York, US: Wiley, 1981.CrossRefMATHGoogle Scholar
  5. [5]
    K. Liano: “Robust Error Measure for Supervised Neural Network Learning with Outliers”. IEEE Transactions on Neural Networks, vol. 7, pp 246–250, 1996.CrossRefGoogle Scholar
  6. [6]
    L. Ljiung, G. Pflug and H. Walk: Stochastic Approximation and Optimization of Random Systems. Basel, CH: Birkhauser Verlag, 1992.CrossRefGoogle Scholar
  7. [7]
    D.E. Rumelhart, G.E. Hinton, R.J. Williams: “Learning internal representations by error propagation”, in Parallel Distributed Processing: Explorations in the Microstructure of Cognition, D.E. Rumelhart and J.L. McClelland, Eds. Cambridge, US: MIT Press, vol 1, pp 318–362, 1986.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Enrico Capobianco
    • 1
  1. 1.CNR — Consiglio Nazionale delle RicercheItaly

Personalised recommendations