title: Maximally informative stimuli and tuning curves for sigmoidal rate-coding neurons and populations.
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.
authors.affiliation: Institute for Telecommunications Research, University of South Australia, SA 5095, Australia. mark.mcdonnell@unisa.edu.au
authors.forename: Mark D
authors.initials: MD
authors.lastname: McDonnell
authors.forename: Nigel G
authors.initials: NG
authors.lastname: Stocks