Implicit encoding of prior probabilities in optimal neural populations

Deep Ganguli, Eero P. Simoncelli

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Optimal coding provides a guiding principle for understanding the representation of sensory variables in neural populations. Here we consider the influence of a prior probability distribution over sensory variables on the optimal allocation of neurons and spikes in a population. We model the spikes of each cell as samples from an independent Poisson process with rate governed by an associated tuning curve. For this response model, we approximate the Fisher information in terms of the density and amplitude of the tuning curves, under the assumption that tuning width varies inversely with cell density. We consider a family of objective functions based on the expected value, over the sensory prior, of a functional of the Fisher information. This family includes lower bounds on mutual information and perceptual discriminability as special cases. In all cases, we find a closed form expression for the optimum, in which the density and gain of the cells in the population are power law functions of the stimulus prior. This also implies a power law relationship between the prior and perceptual discriminability. We show preliminary evidence that the theory successfully predicts the relationship between empirically measured stimulus priors, physiologically measured neural response properties (cell density, tuning widths, and firing rates), and psychophysically measured discrimination thresholds.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 23
Subtitle of host publication24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
StatePublished - 2010
Event24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 - Vancouver, BC, Canada
Duration: Dec 6 2010Dec 9 2010

Publication series

NameAdvances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Other

Other24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
Country/TerritoryCanada
CityVancouver, BC
Period12/6/1012/9/10

ASJC Scopus subject areas

  • Information Systems

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