Adaptive stimulus design for dynamic recurrent neural network models

TL;DR

This paper introduces an optimal experiment design method for estimating parameters of a non-linear, dynamic recurrent neural network model of sensory neurons, improving stimulus-response modeling accuracy.

Contribution

It develops a novel optimal stimulus design scheme that maximizes Fisher Information for dynamic neural models, enhancing parameter estimation accuracy.

Findings

The proposed method outperforms random stimulus approaches in parameter estimation.

Optimal stimuli lead to faster convergence of the neural model parameters.

The approach effectively captures time-dependent neural response features.

Abstract

We present a theoretical application of an optimal experiment design (OED) methodology to the development of mathematical models to describe the stimulus-response relationship of sensory neurons. Although there are a few related studies in the computational neuroscience literature on this topic, most of them are either involving non-linear static maps or simple linear filters cascaded to a static non-linearity. Although the linear filters might be appropriate to demonstrate some aspects of neural processes, the high level of non-linearity in the nature of the stimulus-response data may render them inadequate. In addition, modelling by a static non-linear input - output map may mask important dynamical (time-dependent) features in the response data. Due to all those facts a non-linear continuous time dynamic recurrent neural network that models the excitatory and inhibitory membrane potential dynamics is preferred. The main goal of this research is to estimate the parametric details of this model from the available stimulus-response data. In order to design an efficient estimator an optimal experiment design scheme is proposed which computes a pre-shaped stimulus to maximize a certain measure of Fisher Information Matrix. This measure depends on the estimated values of the parameters in the current step and the optimal stimuli are used in a maximum likelihood estimation procedure to find an estimate of the network parameters. This process works as a loop until a reasonable convergence occurs. The response data is discontinuous as it is composed of the neural spiking instants which is assumed to obey the Poisson statistical distribution. Thus the likelihood functions depend on the Poisson statistics. In order to validate the approach and evaluate its performance, a comparison with another approach on estimation based on randomly generated stimuli is also presented.