A hierarchical Bayes approach to nonlinear time series prediction with neural nets

2002 ◽  
Author(s):  
T. Matsumoto ◽  
H. Hamagishi ◽  
Y. Chonan
Keyword(s):  
Time Series ◽  
Time Series Prediction ◽  
Nonlinear Time Series ◽  
Hierarchical Bayes ◽  
Neural Nets ◽  
Bayes Approach

From data to nonlinear dynamics: Time series prediction via hierarchical Bayes approach

2002 ◽  
Vol 85 (10) ◽  
pp. 71-83
Author(s):  
Takashi Matsumoto ◽  
Hiroaki Hamagishi ◽  
Junjiro Sugi ◽  
Motoki Saito ◽  
Yoshimasa Chonan
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Time Series Prediction ◽  
Hierarchical Bayes ◽  
Bayes Approach

Nonlinear Time-Series Prediction with Missing and Noisy Data

1998 ◽  
Vol 10 (3) ◽  
pp. 731-747 ◽  
Author(s):  
Volker Tresp ◽  
Reimar Hofmann
Keyword(s):  
Time Series ◽  
Stochastic Simulation ◽  
Time Series Prediction ◽  
Noisy Data ◽  
Nonlinear Time Series ◽  
Point Of View ◽  
Data Set ◽  
Sunspot Data ◽  
Error Bars ◽  
Probabilistic Point

We derive solutions for the problem of missing and noisy data in nonlinear time-series prediction from a probabilistic point of view. We discuss different approximations to the solutions—in particular, approximations that require either stochastic simulation or the substitution of a single estimate for the missing data. We show experimentally that commonly used heuristics can lead to suboptimal solutions. We show how error bars for the predictions can be derived and how our results can be applied to K-step prediction. We verify our solutions using two chaotic time series and the sunspot data set. In particular, we show that for K-step prediction, stochastic simulation is superior to simply iterating the predictor.

The Vanishing Gradient Problem During Learning Recurrent Neural Nets and Problem Solutions

1998 ◽  
Vol 06 (02) ◽  
pp. 107-116 ◽  
Author(s):  
Sepp Hochreiter
Keyword(s):  
Time Series ◽  
Time Series Prediction ◽  
Time Lag ◽  
Neural Nets ◽  
Alternative Methods ◽  
Reasonable Time ◽  
Practical Applications ◽  
Learning Time ◽  
Long Time ◽  
Gradient Based

Recurrent nets are in principle capable to store past inputs to produce the currently desired output. Because of this property recurrent nets are used in time series prediction and process control. Practical applications involve temporal dependencies spanning many time steps, e.g. between relevant inputs and desired outputs. In this case, however, gradient based learning methods take too much time. The extremely increased learning time arises because the error vanishes as it gets propagated back. In this article the de-caying error flow is theoretically analyzed. Then methods trying to overcome vanishing gradients are briefly discussed. Finally, experiments comparing conventional algorithms and alternative methods are presented. With advanced methods long time lag problems can be solved in reasonable time.

A Novel Modeling Method Based on Multi-Dimensional Taylor Network and its Application in Time Series Prediction

2014 ◽  
Vol 940 ◽  
pp. 480-484 ◽  
Author(s):  
Yi Lin ◽  
Hong Sen Yan ◽  
Bo Zhou
Keyword(s):  
Time Series ◽  
Prior Knowledge ◽  
Dynamic Characteristics ◽  
Prediction Accuracy ◽  
Time Series Prediction ◽  
Nonlinear Time Series ◽  
Modeling Method ◽  
Input Output ◽  
Output Data ◽  
Bridge Tower

A novel modeling method based on multi-dimensional Taylor network is proposed. The structure and the principle of the multi-dimensional Taylor network are introduced. Based on this, the method is applied in the nonlinear time series prediction based on multi-dimensional Taylor network. It provides a new method to predict the time series, which can describe the dynamic characteristics without prior knowledge and can realize the prediction of the nonlinear time series just with input-output data. An example of predicting the stress data of a large span bridge tower induced by strong typhoon is taken at last in this paper. Results indicate the validity and the better prediction accuracy of this method in nonlinear time series prediction.

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