Summary
We give an overview of the statistical physics of neural networks generating and analysing time series. Storage capacity, bit and sequence generation, prediction error, antipredictable sequences, interacting perceptrons and application to the minority game are discussed. Finally, as a demonstration, a perceptron predicts bit sequences produced by human beings.
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References
J. Hertz, A. Krogh, R.G. Palmer: Introduction to the Theory of Neural Computation ( Addison Wesley, Redwood City 1991 )
A. Engel, C. Van den Broeck: Statistical Mechanics of Learning ( Cambridge University Press, Cambridge 2000 )
W. Kinzel: Comp. Phys. Comm. 121, 86–93 (1999)
M. Biehl, N. Caticha: `Statistical Mechanics of On-line Learning and Generalization’. In: The Handbook of Brain Theory and Neural Networks, ed. by M.A. Arbib ( MIT Press, Berlin 2001 )
M. Opper, W. Kinzel: `Statistical Mechanics of Generalization’. In: Models of Neural Networks III, ed. by E. Domany, J.L. van Hemmen, K. Schulten ( Springer Verlag, Heidelberg 1995 ) p. 151
A. Weigand, N.S. Gershenfeld: Time Series Prediction ( Addison Wesley, Santa Fe 1994 )
E. Eisenstein, I. Kanter, D.A. Kessler, W. Kinzel: Phys. Rev. Letters 74, 6–9 (1995)
I. Kanter, D.A. Kessler, A. Priel, E. Eisenstein: Phys. Rev. Lett. 75, 2614–2617 (1995)
L. Schlaefli: Theorie der Vielfachen Kontinuität, ( Birkhaeuser, Basel 1857 )
E. Gardner: J. Phys. A 21, 257 (1988)
M. Schröder, W. Kinzel, I. Kanter: J. Phys. A 29, 7965 (1996)
L. Ein-Dor, I. Kanter: Phys. Rev. E 57, 6564 (1998)
M. Schröder, W. Kinzel: J. Phys. A 31, 9131–9147 (1998)
A. Priel, I. Kanter: Phys. Rev. E, in press
A. Priel, I. Kanter: Phys. Rev. E 59, 3368–3375 (1999)
A. Priel, I. Kanter: Europhys. Lett. 51, 244–250 (2000)
A. Freking, W. Kinzel, I. Kanter: unpublished
C.M. Bishop: Neural Networks for Pattern Recognition (Oxford University Press, New York 1995 )
H. Zhu, W. Kinzel: Neural Computation 10, 2219–2230 (1998)
W. Kinzel, R. Metzler, I. Kanter: J. Phys. A 33, L141 — L147 (2000)
R. Metzler, W. Kinzel, I. Kanter: Phys. Rev. E 62, 2555 (2000)
Econophysics homepage: http://www.unifr.ch/econophysics/
D. Challet, M. Marsili, R. Zecchina: Phys. Rev. Lett. 84, 1824–1827 (2000)
G. Reents, R. Metzler, W. Kinzel: Cond-mat/0007351 (2000)
W. Kinzel, G. Reents: Physics by Computer ( Springer-Verlag, Heidelberg 1998 )
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Kinzel, W. (2002). Predicting and Generating Time Series by Neural Networks: An Investigation Using Statistical Physics. In: Computational Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04804-7_6
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DOI: https://doi.org/10.1007/978-3-662-04804-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07571-1
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