Maximally informative stimuli and tuning curves for sigmoidal rate-coding neurons and populations |
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Authors: | McDonnell Mark D Stocks Nigel G |
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Institution: | Institute for Telecommunications Research, University of South Australia, SA 5095, Australia. mark.mcdonnell@unisa.edu.au |
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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. |
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