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Predicting Chaotic Time Series by Boosted Recurrent Neural Networks

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Neural Information Processing (ICONIP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4233))

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Abstract

This paper discusses the use of a recent boosting algorithm for recurrent neural networks as a tool to model nonlinear dynamical systems. It combines a large number of RNNs, each of which is generated by training on a different set of examples. This algorithm is based on the boosting algorithm where difficult examples are concentrated on during the learning process. However, unlike the original algorithm, all examples available are taken into account. The ability of the method to internally encode useful information on the underlying process is illustrated by several experiments on well known chaotic processes. Our model is able to find an appropriate internal representation of the underlying process from the observation of a subset of the states variables. We obtain improved prediction performances.

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References

  1. Siegelmann, H.T., Horne, B.G., Giles, C.L.: Computational Capabilities of Recurrent NARX Neural Networks. IEEE Transactions on Systems, Man and Cybernetics 27, 209–214 (1997)

    Google Scholar 

  2. Seidl, D.R., Lorenz, R.D.: A Structure by which a Recurrent Neural Network Can Approximate a Nonlinear Dynamic System. In: International Joint Conference on Neural Networks, pp. 709–714 (1991)

    Google Scholar 

  3. Schapire, R.E.: The Strength of Weak Learnability. Machine Learning 5, 197–227 (1990)

    Google Scholar 

  4. Levin, A.U., Narendra, K.S.: Control of Nonlinear Dynamical Systems Using Neural Networks. IEEE Transactions on Neural Networks 7, 30–42 (1996)

    Article  Google Scholar 

  5. Oliveira, K.A., Vannucci, A., Silva, E.C.: Using Artificial Neural Networks to Forecast Chaotic Time Series. Physica A, 393–399 (2000)

    Google Scholar 

  6. Tronci, S., Giona, M., Baratti, R.: Reconstruction of Chaotic Time Series by Neural Models: a Case Study. Neurocomputing 55, 581–591 (2003)

    Article  Google Scholar 

  7. Connor, J.T., Martin, R.D., Atlas, L.E.: Recurrent Neural Networks and Robust Time Series Prediction. IEEE Transactions on Neural networks 5, 240–254 (1994)

    Article  Google Scholar 

  8. Takens, F.: Detecting Strange Attractors in Turbulence. In: Dynamical Systems and Turbulence, pp. 366–381. Springer, Heidelberg (1980)

    Google Scholar 

  9. Leontaritis, I.J., Billings, S.: Input-Output Parametric Models for Non-Linear Systems. International Journal of Control 41, 303–344 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  10. Aussem, A.: Dynamical Recurrent Neural Networks: Towards Prediction and Modelling of Dynamical Systems. Neurocomputing 28, 207–232 (1999)

    Article  Google Scholar 

  11. Boné, R., Crucianu, M., Asselin de Beauville, J.-P.: Learning Long-Term Dependencies by the Selective Addition of Time-Delayed Connections to Recurrent Neural Networks. NeuroComputing 48, 251–266 (2002)

    Article  MATH  Google Scholar 

  12. Freund, Y., Schapire, R.E.: A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting. Journal of Computer and System Sciences 55, 119–139 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ridgeway, G., Madigan, D., Richardson, T.: Boosting Methodology for Regression Problems. Artificial Intelligence and Statistics, 152–161 (1999)

    Google Scholar 

  14. Mason, L., Baxter, J., Bartlett, P.L., Frean, M.: Functional Gradient Techniques for Combining Hypotheses. In: Smola, A.J., et al. (eds.) Advances in Large Margin Classifiers, pp. 221–247. MIT Press, Cambridge (1999)

    Google Scholar 

  15. Duffy, N., Helmbold, D.: Boosting Methods for Regression. Machine Learning 47, 153–200 (2002)

    Article  MATH  Google Scholar 

  16. Cook, G.D., Robinson, A.J.: Boosting the Performance of Connectionist Large Vocabulary Speech Recognition. In: International Conference in Spoken Language Processing, pp. 1305–1308 (1996)

    Google Scholar 

  17. Avnimelech, R., Intrator, N.: Boosting Regression Estimators. Neural Computation 11, 491–513 (1999)

    Google Scholar 

  18. Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning Internal Representations by Error Propagation. In: Rumelhart, D.E., McClelland, J. (eds.) Parallel Distributed Processing: Explorations in the Microstructure of Cognition, pp. 318–362. MIT Press, Cambridge (1986)

    Google Scholar 

  19. Freund, Y.: Boosting a Weak Learning Algorithm by Majority. In: Workshop on Computational Learning Theory, pp. 202–216 (1990)

    Google Scholar 

  20. Drucker, H.: Boosting Using Neural Nets. In: Sharkey, A. (ed.) Combining Artificial Neural Nets: Ensemble and Modular Learning, pp. 51–77. Springer, Heidelberg (1999)

    Google Scholar 

  21. Boné, R., Assaad, M., Crucianu, M.: Boosting Recurrent Neural Networks for Time Series Prediction. In: International Conference on Artificial Neural Networks and Genetic Algorithms, pp. 18–22 (2003)

    Google Scholar 

  22. Mackey, M., Glass, L.: Oscillations and Chaos in Physiological Control Systems. Science, 197–287 (1977)

    Google Scholar 

  23. Casdagli, M.: Nonlinear Prediction of Chaotic Time Series. Physica 35D, 335–356 (1989)

    Google Scholar 

  24. Back, A., Wan, E.A., Lawrence, S., Tsoi, A.C.: A Unifying View of some Training Algorithms for Multilayer Perceptrons with FIR Filter Synapses. In: Neural Networks for Signal Processing IV, pp. 146–154 (1994)

    Google Scholar 

  25. Gers, F., Eck, D., Schmidhuber, J.: Applying LSTM to Time Series Predictable Through Time-Window Approaches. In: International Conference on Artificial Neural Networks, pp. 669–675 (2001)

    Google Scholar 

  26. Ott, E.: Chaos in Dynamical Sytems. Cambridge University Press, Cambridge (1993)

    Google Scholar 

  27. Wan, E.A.: Time Series Prediction by Using a Connection Network with Internal Delay Lines. In: Weigend, A.S., Gershenfeld, N.A. (eds.) Time Series Prediction: Forecasting the Future and Understanding the Past, pp. 195–217. Addison-Wesley, Reading (1994)

    Google Scholar 

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Assaad, M., Boné, R., Cardot, H. (2006). Predicting Chaotic Time Series by Boosted Recurrent Neural Networks. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893257_92

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  • DOI: https://doi.org/10.1007/11893257_92

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46481-5

  • Online ISBN: 978-3-540-46482-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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