TY - JOUR

T1 - Time series prediction by feedforward neural networks - Is it difficult?

AU - Rosen-Zvi, Michal

AU - Kanter, Ido

AU - Kinzel, Wolfgang

PY - 2003/4/25

Y1 - 2003/4/25

N2 - The difficulties that a neural network faces when trying to learn from a quasi-periodic time series are studied analytically using a teacher-student scenario where the random input is divided into two macroscopic regions with different variances, 1 and 1/γ2 (γ ≫ 1). The generalization error is found to decrease as ∈g ∝ exp(-α/γ2), where α is the number of examples per input dimension. In contradiction to this very slow vanishing generalization error, the next output prediction is found to be almost free of mistakes. This picture is consistent with learning quasi-periodic time series produced by feedforward neural networks, which is dominated by enhanced components of the Fourier spectrum of the input. Simulation results are in good agreement with the analytical results.

AB - The difficulties that a neural network faces when trying to learn from a quasi-periodic time series are studied analytically using a teacher-student scenario where the random input is divided into two macroscopic regions with different variances, 1 and 1/γ2 (γ ≫ 1). The generalization error is found to decrease as ∈g ∝ exp(-α/γ2), where α is the number of examples per input dimension. In contradiction to this very slow vanishing generalization error, the next output prediction is found to be almost free of mistakes. This picture is consistent with learning quasi-periodic time series produced by feedforward neural networks, which is dominated by enhanced components of the Fourier spectrum of the input. Simulation results are in good agreement with the analytical results.

UR - http://www.scopus.com/inward/record.url?scp=0038745778&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/16/305

DO - 10.1088/0305-4470/36/16/305

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AN - SCOPUS:0038745778

SN - 0305-4470

VL - 36

SP - 4543

EP - 4550

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 16

ER -