Fitting a recurrent dynamical neural network to neural spiking data: Tackling with the sigmoidal gain function issues

This is a continuation of a recent study on the modeling of the information coding in sensory system in the brain. The data from a sensory neurons are available as discrete spike timings with no amplitude information. In the simulations, these are generated from a data generator model which has certain differences from the model being estimated. The model under consideration is simpler than the one used as a data generator as it has no sigmoidal gain function parameters. This choice is based on a suggestion from a recent study which states that inclusion of gain functions to the estimation algorithm increases issues such as parameter confounding which leads to performance degradation issues like increased or unpredictable variance changes with different stimuli configurations. To resolve this issue we consider a more generic model that has no sigmoidal gain functions to be estimated. Like that of the first research, we applied a Fourier series stimulus to both data generator and the estimated network. In order to test the performance of the proposed scheme, we have repeated the simulations with different sample sizes, stimulus component counts, amplitude and base frequencies. Mean values of estimation are presented as tables and the statistical analysis results are presented in graphical forms. In addition, since we do not have any true parameter data (for the estimated model) we compare the firing rate responses of both data generator and estimated models to different stimuli. It appeared that the responses of both models are almost the same.