Efficient sensory coding of multidimensional stimuli
Fig 4
Analysis of how lower-dimensional measurements of tuning curve properties (1-D gain and tuning width) relate to the higher-dimensional stimulus probability.
Four example neuronal populations are shown, which correspond to the probability distributions and optimized mappings in Fig 3 (re-plotted in the top row). We simulated a set of 1-D experiments by selecting a single value for either s1 or s2 and measuring the response gain (maximum response) and tuning sharpness (inverse of the full width half maximum) of a set of neurons within this ‘slice’ (σ pre-warping was 0.05). This method simulates what the measured neuronal gain and tuning bandwidth would be in an experiment in which one stimulus feature was held constant and the other was varied. (A-D) For each of the illustrated populations, these panels plot the 1-D tuning sharpness as a function of probability, for a sample of neurons (400-700 neurons). Samples that were drawn by holding s1 constant are shown in red, and samples drawn by holding s2 constant are in black. (E-H) These panels plot the 1-D response gain as a function of stimulus probability, as in the panels above. (I,J) We repeated these simulations 500 times for randomly generated 2-D stimulus probability distributions and calculated the correlation between gain/tuning and probability. Each probability distribution was a zero-centered, bivariate Gaussian with a random orientation and major/minor σ drawn uniformly from 0.1-0.4. For each simulation, the tuning curves were modeled as isotropic Gaussians with σ drawn uniformly from 0.03-0.07. A random 1-D slice was selected, and 25 neurons were sampled. P-values indicate the results of a Wilcoxon signed rank test determining whether the median correlation was significantly different from zero.