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

摘要

We present a theoretical study aiming at model fitting for sensory neurons.Conventional neural network training approaches are not applicable to thisproblem due to lack of continuous data. Although the stimulus can be consideredas a smooth time dependent variable, the associated response will be a set ofneural spike timings (roughly the instants of successive action potentialpeaks) which have no amplitude information. A recurrent neural network modelcan be fitted to such a stimulus-response data pair by using maximum likelihoodestimation method where the likelihood function is derived from Poissonstatistics of neural spiking. The universal approximation feature of therecurrent dynamical neuron network models allow us to describeexcitatory-inhibitory characteristics of an actual sensory neural network withany desired number of neurons. The stimulus data is generated by a PhasedCosine Fourier series having fixed amplitude and frequency but a randomly shotphase. Various values of amplitude, stimulus component size and sample size areapplied in order to examine the effect of stimulus to the identificationprocess. Results are presented in tabular form at the end of this text.