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Orthogonal Echo State Networks and Stochastic Evaluations of Likelihoods

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Abstract

We report about probabilistic likelihood estimates that are performed on time series using an echo state network with orthogonal recurrent connectivity. The results from tests using synthetic stochastic input time series with temporal inference indicate that the capability of the network to infer depends on the balance between input strength and recurrent activity. This balance has an influence on the network with regard to the quality of inference from the short-term input history versus inference that accounts for influences that date back a long time. Sensitivity of such networks against noise and the finite accuracy of network states in the recurrent layer are investigated. In addition, a measure based on mutual information between the output time series and the reservoir is introduced. Finally, different types of recurrent connectivity are evaluated. Orthogonal matrices not only show the best results of all investigated connectivity types overall but also in the way how the network performance scales with the size of the recurrent layer.

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Notes

  1. One possible explanation is that the parameter β affects the total activity of the network |x t |2. In the case of low activity, the non-linear component of the sigmoid transfer function is tiny. Thus, the resulting network is nearly a linear ESN, for which the highest values of memory capacity (MC)—near the theoretical limit—have already been found earlier [8]. On the other hand, the non-linear components are necessary to distinguish different vectors in the Hilbert space in order to have a sufficiently good approximation to model the probabilities.

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Acknowledgements

N.M.M. thanks Oliver Obst for his previous work and the Doctoral Program in Cognitive Sciences at the National Chung Cheng University for setting up an interesting forum for discussions. Earlier preparations for this paper had been funded by the National Science Council of Taiwan and the Ministry of Science and Technology of Taiwan.

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  1. Adaptive Embedded Systems & Robotics Laboratory, Department of Electrical Engineering and Advanced Institute of Manufacturing with High-tech Innovations (AIM-HI), National Chung Cheng University, Min-Hsiung, Chia-Yi, Taiwan

    N. Michael Mayer & Ying-Hao Yu

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  1. N. Michael Mayer
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  2. Ying-Hao Yu
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Correspondence to N. Michael Mayer.

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Mayer, N.M., Yu, YH. Orthogonal Echo State Networks and Stochastic Evaluations of Likelihoods. Cogn Comput 9, 379–390 (2017). https://doi.org/10.1007/s12559-017-9466-4

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