Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7700))

Abstract

The purpose of this paper is to give a guidance in neural network modeling. Starting with the preprocessing of the data, we discuss different types of network architecture and show how these can be combined effectively. We analyze several cost functions to avoid unstable learning due to outliers and heteroscedasticity. The Observer - Observation Dilemma is solved by forcing the network to construct smooth approximation functions. Furthermore, we propose some pruning algorithms to optimize the network architecture. All these features and techniques are linked up to a complete and consistent training procedure (see figure 17.25 for an overview), such that the synergy of the methods is maximized.

Previously published in: Orr, G.B. and Müller, K.-R. (Eds.): LNCS 1524, ISBN 978-3-540-65311-0 (1998).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ackley, D.H., Hinton, G.E., Sejnowski, T.J.: A learning algorithm for Boltzmann machines. Cognitive Science 9, 147–169 (1985); Reprinted in [2]

    Google Scholar 

  2. Anderson, J.A., Rosenfeld, E. (eds.): Neurocomputing: Foundations of Research. The MIT Press, Cambridge (1988)

    Google Scholar 

  3. Bishop, C.M.: Neural Networks for Pattern Recognition. Clarendon Press, Oxford (1995)

    MATH  Google Scholar 

  4. Breiman, L.: Bagging predictors. Technical Report TR No. 421, Department of Statistics, University of California (1994)

    Google Scholar 

  5. Bunke, H., Bunke, O.: Nonlinear Regression, Functional Analysis and Robust Methods, vol. 2. John Wiley and Sons (1989)

    Google Scholar 

  6. Caruana, R.: Multitask learning. Machine Learning 28, 41 (1997)

    Article  Google Scholar 

  7. Elton, E.J., Gruber, M.J.: Modern Portfolio Theory and Investment Analysis. John Wiley & Sons (1995)

    Google Scholar 

  8. Finnoff, W., Hergert, F., Zimmermann, H.G.: Improving generalization performance by nonconvergent model selection methods. In: Aleksander, I., Taylor, J. (eds.) Proc. of the Inter. Conference on Artificial Neural Networks, ICANN 1992, vol. 2, pp. 233–236 (1992)

    Google Scholar 

  9. Finnoff, W., Hergert, F., Zimmermann, H.G.: Neuronale Lernverfahren mit variabler Schrittweite, Tech. report, Siemens AG (1993)

    Google Scholar 

  10. Flake, G.W.: Square Unit Augmented, Radially Extended, Multilayer Perceptrons. In: Orr, G.B., Müller, K.-R. (eds.) NN: Tricks of the Trade, 1st edn. LNCS, vol. 7700, pp. 143–161. Springer, Heidelberg (2012)

    Google Scholar 

  11. Gershenfeld, N.A.: An experimentalist’s introduction to the observation of dynamical systems. In: Hao, B.L. (ed.) Directions in Chaos, vol. 2, pp. 310–384. World Scientific, Singapore (1989)

    Google Scholar 

  12. Herve, P., Naim, P., Zimmermann, H.G.: Advanced Adaptive Architectures for Asset Allocation: A Trial Application. In: Forecasting Financial Markets (1996)

    Google Scholar 

  13. Hochreiter, S., Schmidhuber, J.: Flat minima. Neural Computation 9(1), 1–42 (1997)

    Article  MATH  Google Scholar 

  14. Hornik, K.: Approximation Capabilities of Multilayer Feedforward Networks. Neural Networks 4, 251–257 (1991)

    Article  Google Scholar 

  15. le Cun, Y., Denker, J.S., Solla, S.A.: Optimal brain damage. In: Touretzky, D.S. (ed.) Advances in Neural Information Processing Systems, NIPS 1989, vol. 2, pp. 598–605. Morgan Kaufmann, San Mateo (1990)

    Google Scholar 

  16. Moody, J.E., Rögnvaldsson, T.S.: Smoothing regularizers for projective basis function networks. In: Mozer, M.C., Jordan, M.I., Petsche, T. (eds.) Advances in Neural Information Processing Systems, vol. 9, p. 585. The MIT Press (1997)

    Google Scholar 

  17. Williams, P.M.: Using Neural Networks to Model Conditional Multivariate Densities. Technical Report CSRP 371, School of Cognitive and Computing Sciences, Univ. of Sussex (February 1995)

    Google Scholar 

  18. Neuneier, R.: Optimal asset allocation using adaptive dynamic programming. In: Advances in Neural Information Processing Systems, vol. 8. MIT Press (1996)

    Google Scholar 

  19. Neuneier, R.: Optimale Investitionsentscheidungen mit Neuronalen Netzen. PhD thesis, Universität Kaiserslautern, Institut für Informatik (1998)

    Google Scholar 

  20. Neuneier, R., Finnoff, W., Hergert, F., Ormoneit, D.: Estimation of Conditional Densities: A Comparison of Neural Network Approaches. In: Intern. Conf. on Artificial Neural Networks, ICANN, vol. 1, pp. 689–692. Springer (1994)

    Google Scholar 

  21. Nix, D.A., Weigend, A.S.: Estimating the mean and variance of the target probability distribution. In: World Congress of Neural Networks. Lawrence Erlbaum Associates (1994)

    Google Scholar 

  22. Ormoneit, D.: Estimation of Probability Densities using Neural Networks. Master’s thesis, Fakultät für Informatik, Technische Universität München (1993)

    Google Scholar 

  23. Papoulis, A.: Probability, Random Variables, and Stochastic Processes, 3rd edn. McGraw Hill, Inc. (1991)

    Google Scholar 

  24. Perrone, M.P.: Improving Regression Estimates: Averaging Methods for Variance Reduction with Extensions to General Convex Measure Optimization. PhD thesis, Brown University (1993)

    Google Scholar 

  25. Refenes, A.P. (ed.): Neural Networks in the Capital Market. Wiley & Sons (1994)

    Google Scholar 

  26. Sanger, T.D.: Optimal unsupervised learning in a single-layer linear feedforward network. Neural Networks 2, 459–473 (1989)

    Article  Google Scholar 

  27. Seber, G.A.F., Wild, C.J.: Nonlinear Regression. John Wiley & Sons, New York (1989)

    Book  MATH  Google Scholar 

  28. Srivastava, A.N., Weigend, A.S.: Computing the probability density in connectionist regression. In: Marinaro, M., Morasso, P.G. (eds.) Proceedings of the International Conference on Artificial Neural Networks, Sorrento, Italy (ICANN 1994), pp. 685–688. Springer (1994); Also in Proceedings of the IEEE International Conference on Neural Networks, Orlando, FL (IEEE–ICNN 1994), pp. 3786–3789. IEEE Press (1994)

    Google Scholar 

  29. Takens, F.: Detecting Strange Attractors in Turbulence. In: Rand, D.A., Young, L.S. (eds.) Dynamical Systems and Turbulence. Lecture Notes in Mathematics, vol. 898, pp. 366–381. Springer (1981)

    Google Scholar 

  30. Tang, B., Hsieh, W., Tangang, F.: Clearning neural networks with continuity constraints for prediction of noisy time series. In: Progres in Neural Information Processing (ICONIP 1996), pp. 722–725. Springer, Berlin (1996)

    Google Scholar 

  31. Tresp, V., Neuneier, R., Zimmermann, H.G.: Early brain damage. In: Advances in Neural Information Processing Systems, vol. 9. MIT Press (1997)

    Google Scholar 

  32. Weigend, A.S., Zimmermann, H.G.: Exploiting local relations as soft constraints to improve forecasting. Computational Intelligence in Finance 6(1) (January 1998)

    Google Scholar 

  33. Weigend, A.S., Zimmermann, H.G., Neuneier, R.: The observer-observation dilemma in neuro-forecasting: Reliable models from unreliable data through clearning. In: Freedman, R. (ed.) AI Applications on Wall Street, pp. 308–317. Software Engineering Press, New York (1995)

    Google Scholar 

  34. Weigend, A.S., Rumelhart, D.E., Huberman, B.A.: Generalization by weight-elimination with application to forecasting. In: Lippmann, R.P., Moody, J.E., Touretzky, D.S. (eds.) Advances in Neural Information Processing Systems, vol. 3, pp. 875–882. Morgan Kaufmann, San Mateo (1991)

    Google Scholar 

  35. White, H.: Parametrical statistical estimation with artificial neural networks. Technical report, University of California, San Diego (1991)

    Google Scholar 

  36. Zimmermann, H.G., Weigend, A.S.: Representing dynamical systems in feed-forward networks: A six layer architecture. In: Weigend, A.S., Abu-Mostafa, Y., Refenes, A.-P.N. (eds.) Decision Technologies for Financial Engineering: Proceedings of the Fourth International Conference on Neural Networks in the Capital Markets (NNCM 1996). World Scientific, Singapore (1997)

    Google Scholar 

  37. Zimmermann, H.G.: Neuronale Netze als Entscheidungskalkül. In: Rehkugler, H., Zimmermann, H.G. (eds.) Neuronale Netze in der Ökonomie. Verlag Franz Vahlen (1994)

    Google Scholar 

  38. Zimmermann, H.G., Neuneier, R.: The observer-observation dilemma in neuro-forecasting. In: Advances in Neural Information Processing Systems, vol. 10. MIT Press (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Neuneier, R., Zimmermann, H.G. (2012). How to Train Neural Networks. In: Montavon, G., Orr, G.B., Müller, KR. (eds) Neural Networks: Tricks of the Trade. Lecture Notes in Computer Science, vol 7700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35289-8_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-35289-8_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35288-1

  • Online ISBN: 978-3-642-35289-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics