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Keith May, Li Zhaoping; Contrast-response functions, Fisher information, and contrast decoding performance. Journal of Vision 2011;11(11):1172. doi: 10.1167/11.11.1172.
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© ARVO (1962-2015); The Authors (2016-present)
Using maximum a posteriori decoding of stimulus contrast, Clatworthy, Chirimuuta, Lauritzen and Tolhurst (2003, Vision Research, 43, 1983–2001) discovered many characteristics of the relationship between the contrast-response function [described by the Naka-Rushton function, r = rmaxcq(c50q + cq)] and contrast identification accuracy. Their decoding method is optimal, but laborious to implement, and gives little insight into why these characteristics arise, or how general they are. If the spike count is not too low, the Fisher information provides a good analytical approximation of optimal decoding accuracy. We show how to calculate the Fisher information for Clatworthy et al.'s doubly stochastic Poisson process, and derive equations that explain many of their observations regarding single neurons, e.g. that accuracy peaks “slightly below the neuron's c″50 (Clatworthy et al., p. 1989) – we show that it peaks at the contrast for which mean response is rmax/3. Fisher information provides a closer estimate of optimal decoding accuracy for neural populations than for single neurons because of the higher total spike count. We show that, for a population of N ≥ 8 Poisson-spiking neurons with q = 2 and c50 values evenly distributed across the log contrast range, log10c E [−3, 0.1], Fisher information very closely approximates optimal contrast decoding accuracy when N × rmax is greater than about 100 spikes; in these conditions, decoding accuracy is very close to being proportional to N × rmax. We also investigate the effect of supersaturation, whereby the contrast-response function peaks and then declines with increasing contrast. Contrary to the proposal that supersaturating neurons provide a suboptimal contrast code [Peirce, 2007, Journal of Vision, 7(6):13, 1–10], we show that supersaturation improves contrast decoding accuracy for neural populations, while also reducing metabolic costs.
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