Predicting and Generating Time Series by Neural Networks: An Investigation Using Statistical Physics

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.

[1]  A. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[2]  Franklin A. Graybill,et al.  Introduction to The theory , 1974 .

[3]  L. Ein-Dor,et al.  Time series generation by multilayer networks , 1998 .

[4]  Christian Van den Broeck,et al.  Statistical Mechanics of Learning , 2001 .

[5]  Wolfgang Kinzel,et al.  Antipredictable Sequences: Harder to Predict Than Random Sequences , 1998, Neural Computation.

[6]  I. Kanter,et al.  Training a perceptron by a bit sequence: storage capacity , 1996 .

[7]  W. Kinzel,et al.  Limit cycles of a perceptron , 1997, cond-mat/9710010.

[8]  E. Gardner.  The space of interactions in neural network models , 1988 .

[9]  R. Metzler,et al.  Dynamics of interacting neural networks , 1999 .

[10]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[11]  Zecchina,et al.  Statistical mechanics of systems with heterogeneous agents: minority games , 1999, Physical review letters.

[12]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[13]  Manfred Opper,et al.  Statistical mechanics of generalization , 1998 .

[14]  L. Schläfli.  Theorie der vielfachen Kontinuität , 1901 .

[15]  Wolfgang Kinzel.  Statistical physics of neural networks , 1999 .

[16]  Michael Biehl,et al.  Statistical Mechanics of On{line Learning and Generalization the Handbook of Brain Theory and Neural Networks , 2003 .

[17]  Eytan Domany,et al.  Models of Neural Networks I , 1991 .

[18]  Martin Clajus,et al.  Physics by Computer , 1997 .

[19]  Kanter,et al.  Generation and prediction of time series by a neural network. , 1995, Physical review letters.

[20]  Kanter,et al.  Learning and generation of long-range correlated sequences , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[22]  Manfred Opper,et al.  Statistical mechanics of learning in the presence of outliers , 1998 .

[23]  I. Kanter,et al.  Robust chaos generation by a perceptron , 2000 .

[24]  Kanter,et al.  Analytical study of time series generation by feed-forward networks. , 1995, Physical review letters.

[25]  Secure and linear cryptosystems using error-correcting codes , 2000, cond-mat/0008392.

[26]  Andreas S. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[27]  G. Reents,et al.  A stochastic strategy for the minority game , 2001 .

[28]  I Kanter,et al.  Interacting neural networks. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.