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Fitting of dynamic recurrent neural network models to sensory stimulus-response data

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Abstract

We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a smooth time-dependent variable, the associated response will be a set of neural spike timings (roughly the instants of successive action potential peaks) that have no amplitude information. A recurrent neural network model can be fitted to such a stimulus-response data pair by using the maximum likelihood estimation method where the likelihood function is derived from Poisson statistics of neural spiking. The universal approximation feature of the recurrent dynamical neuron network models allows us to describe excitatory-inhibitory characteristics of an actual sensory neural network with any desired number of neurons. The stimulus data are generated by a phased cosine Fourier series having a fixed amplitude and frequency but a randomly shot phase. Various values of amplitude, stimulus component size, and sample size are applied in order to examine the effect of the stimulus to the identification process. Results are presented in tabular and graphical forms at the end of this text. In addition, to demonstrate the success of this research, a study involving the same model, nominal parameters and stimulus structure, and another study that works on different models are compared to that of this research.

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Funding

This study was partially supported by the Turkish Scientific and Technological Research Council’s DB-2219 Grant Program.

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Atilim University, Kizilcasar Mahallesi, Incek, Golbasi, Ankara, 06836, Turkey

    R. Ozgur Doruk

  2. Department of Biomedical Engineering, Johns Hopkins School of Medicine, 720 Rutland Avenue, Traylor 407, Baltimore, MD, 21205, USA

    Kechen Zhang

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  1. R. Ozgur Doruk
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  2. Kechen Zhang
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Correspondence to R. Ozgur Doruk.

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The authors declare that they have no conflict of interest.

Additional information

This work was partially supported by the Turkish Scientific and Technological Research Council (TÜBİTAK) 2219 Research Program. The computational facilities needed in this research were provided by the High Performance Computing (HPC) center TRUBA/TR-GRID owned by the National Academic Information Center (ULAKBIM) of TURKEY. The work started at Johns Hopkins University School of Medicine while the corresponding author (R.O. DORUK) was employed there. The work continued in Atilim University after 2014 where the corresponding author is still employed.

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Doruk, R.O., Zhang, K. Fitting of dynamic recurrent neural network models to sensory stimulus-response data. J Biol Phys 44, 449–469 (2018). https://doi.org/10.1007/s10867-018-9501-z

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  • DOI: https://doi.org/10.1007/s10867-018-9501-z

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