Fitting a Recurrent Dynamical Neural Network To Neural Spiking Data: Tackling the Sigmoidal Gain Function Issues

Abstract

This is a continuation of a recent study (Doruk RO, Zhang K. Fitting of dynamic recurrent neural networkmodels to sensory stimulus-response data. J Biol Phys 2018; 44: 449-469), where a continuous time dynamical recurrentneural network is fitted to neural spiking data. In this research, we address the issues arising from the inclusion ofsigmoidal gain function parameters to the estimation algorithm. The neural spiking data will be obtained from the samemodel as that of Doruk and Zhang, but we propose a different model for identification. This will also be a continuoustime recurrent neural network, but with generic sigmoidal gains. The simulation framework and estimation algorithmsare kept similar to that of Doruk and Zhang so that we can have a solid base to compare the results. We evaluatethe estimation performance in two different ways. First, we compare the firing rate responses of the original and theestimated model. We find that responses of both models to the same stimuli are similar. Secondly, we evaluate variationsof the standard deviations of the estimates against a number of samples and stimulus parameters. They show a similarpattern to that of Doruk and Zhang. We thus conclude that our model serves as a reasonable alternative provided thatfiring rate is the response of interest (to any stimulus).