Maximally Informative Stimuli and Tuning Curves for Sigmoidal Rate-Coding Neurons and Populations

TL;DR

This paper introduces a method to derive optimal sigmoidal tuning curves for neural systems with low variability, linking stimulus distribution, Fisher information, and mutual information to maximize neural coding efficiency.

Contribution

It provides a general framework for deriving maximally informative tuning curves based on the stimulus distribution and neural variability, utilizing Fisher information and Jeffrey's prior.

Findings

Optimal tuning curves are nonlinear functions of stimulus CDF.

Maximum mutual information occurs with constant Fisher information only for uniform stimulus distribution.

Analyzed sub-Poisson binomial firing statistics as a case study.

Abstract

A general method for deriving maximally informative sigmoidal tuning curves for neural systems with small normalized variability is presented. The optimal tuning curve is a nonlinear function of the cumulative distribution function of the stimulus and depends on the mean-variance relationship of the neural system. The derivation is based on a known relationship between Shannon's mutual information and Fisher information, and the optimality of Jeffrey's prior. It relies on the existence of closed-form solutions to the converse problem of optimizing the stimulus distribution for a given tuning curve. It is shown that maximum mutual information corresponds to constant Fisher information only if the stimulus is uniformly distributed. As an example, the case of sub-Poisson binomial firing statistics is analyzed in detail.