The efficient coding hypothesis asserts that sensory systems evolved to maximize information transmitted to the brain about the environment. We develop a precise and testable form of this hypothesis in the context of encoding a sensory variable in the responses of a population of noisy neurons, each characterized by a tuning curve. We obtain a closed form solution for the information maximizing tuning curves as a function of the prior probability of sensory variables encountered in the environment. The solution states that more cells with narrower tuning widths should be allocated to encode higher probability stimuli. We extend our result to predict the discrimination performance of a perceptual system operating on the efficient neural representation, and find that the best achievable discrimination thresholds are inversely proportional to the sensory prior. The predicted relationships between empirically measured stimulus priors, physiological tuning properties, and perceptual discriminability are remarkably well matched to data obtained for two auditory and three visual variables.
We also derive a novel decoder that performs Bayesian estimation by utilizing the prior information embedded in the preferred stimuli of the optimal tuning curves. Similar to the population vector, our decoder computes weighted averages of the preferred stimuli. However, the firing rates are not used directly as weights, but are first convolved with a linear filter then exponentiated. We map this simple cascade onto a compact, biologically plausible neural circuit.
The results in this thesis provide a strong link between two dominant theories in sensory neuroscience -- efficient coding and Bayesian estimation -- and suggest how to relate both ideas directly to data from physiological and perceptual experiments.