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