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).
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References
Ackley, D.H., Hinton, G.E., Sejnowski, T.J.: A learning algorithm for Boltzmann machines. Cognitive Science 9, 147–169 (1985); Reprinted in [2]
Anderson, J.A., Rosenfeld, E. (eds.): Neurocomputing: Foundations of Research. The MIT Press, Cambridge (1988)
Bishop, C.M.: Neural Networks for Pattern Recognition. Clarendon Press, Oxford (1995)
Breiman, L.: Bagging predictors. Technical Report TR No. 421, Department of Statistics, University of California (1994)
Bunke, H., Bunke, O.: Nonlinear Regression, Functional Analysis and Robust Methods, vol. 2. John Wiley and Sons (1989)
Caruana, R.: Multitask learning. Machine Learning 28, 41 (1997)
Elton, E.J., Gruber, M.J.: Modern Portfolio Theory and Investment Analysis. John Wiley & Sons (1995)
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)
Finnoff, W., Hergert, F., Zimmermann, H.G.: Neuronale Lernverfahren mit variabler Schrittweite, Tech. report, Siemens AG (1993)
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)
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)
Herve, P., Naim, P., Zimmermann, H.G.: Advanced Adaptive Architectures for Asset Allocation: A Trial Application. In: Forecasting Financial Markets (1996)
Hochreiter, S., Schmidhuber, J.: Flat minima. Neural Computation 9(1), 1–42 (1997)
Hornik, K.: Approximation Capabilities of Multilayer Feedforward Networks. Neural Networks 4, 251–257 (1991)
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)
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)
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)
Neuneier, R.: Optimal asset allocation using adaptive dynamic programming. In: Advances in Neural Information Processing Systems, vol. 8. MIT Press (1996)
Neuneier, R.: Optimale Investitionsentscheidungen mit Neuronalen Netzen. PhD thesis, Universität Kaiserslautern, Institut für Informatik (1998)
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)
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)
Ormoneit, D.: Estimation of Probability Densities using Neural Networks. Master’s thesis, Fakultät für Informatik, Technische Universität München (1993)
Papoulis, A.: Probability, Random Variables, and Stochastic Processes, 3rd edn. McGraw Hill, Inc. (1991)
Perrone, M.P.: Improving Regression Estimates: Averaging Methods for Variance Reduction with Extensions to General Convex Measure Optimization. PhD thesis, Brown University (1993)
Refenes, A.P. (ed.): Neural Networks in the Capital Market. Wiley & Sons (1994)
Sanger, T.D.: Optimal unsupervised learning in a single-layer linear feedforward network. Neural Networks 2, 459–473 (1989)
Seber, G.A.F., Wild, C.J.: Nonlinear Regression. John Wiley & Sons, New York (1989)
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)
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)
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)
Tresp, V., Neuneier, R., Zimmermann, H.G.: Early brain damage. In: Advances in Neural Information Processing Systems, vol. 9. MIT Press (1997)
Weigend, A.S., Zimmermann, H.G.: Exploiting local relations as soft constraints to improve forecasting. Computational Intelligence in Finance 6(1) (January 1998)
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)
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)
White, H.: Parametrical statistical estimation with artificial neural networks. Technical report, University of California, San Diego (1991)
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)
Zimmermann, H.G.: Neuronale Netze als Entscheidungskalkül. In: Rehkugler, H., Zimmermann, H.G. (eds.) Neuronale Netze in der Ökonomie. Verlag Franz Vahlen (1994)
Zimmermann, H.G., Neuneier, R.: The observer-observation dilemma in neuro-forecasting. In: Advances in Neural Information Processing Systems, vol. 10. MIT Press (1998)
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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
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