Journal of Biological Physics

, Volume 44, Issue 3, pp 449–469 | Cite as

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

  • R. Ozgur DorukEmail author
  • Kechen Zhang
Original Paper


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.


Sensory neurons Recurrent neural network Excitatory neuron Inhibitory neuron Neural spiking Maximum likelihood estimation 


Funding Information

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

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical and Electronics EngineeringAtilim UniversityGolbasiTurkey
  2. 2.Department of Biomedical EngineeringJohns Hopkins School of MedicineBaltimoreUSA

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