The neurally plausible maximum likelihood decoder of Jazayeri and Movshon (2006) failed in the same ways shown in Figure 4F. Because the maximum likelihood decoder in Equation 9 was designed to work with Gaussian noise in the model neurons, we verified that we obtained the same results with Entinostat chemical structure either Gaussian
or Poisson noise. Also, we verified that MT-pursuit correlations from the maximum-likelihood decoder we used were smaller than those resulting from a maximum-likelihood decoder that ignores neuron-neuron correlations (data not shown). We think the maximum-likelihood decoding model fails to compensate fully for the correlated responses because it knows only the structure of Androgen Receptor antagonist the correlations but cannot fully anticipate the exact correlations in any given run of the model. The properties of the decoder are the main determinant of the structure of the MT-pursuit correlations; decorrelation of the neural populations that contribute to the numerator and denominator is the key factor for reproducing our data qualitatively. The properties of the MT population affect the magnitude but not the structure
of the model’s MT-pursuit correlations for all decoders. The magnitude increased with (1) increases in the magnitude of neuron-neuron correlations in MT, (2) increases very in the breadth of neuron-neuron correlations as a function of differences in preferred speed or direction of a pair of neurons, and (3) increases in the amplitude of the population response. MT-pursuit correlations effectively
vanish for model MT populations with uniform, rather than structured, neuron-neuron correlations, or model MT populations without neuron-neuron correlations. We subtracted these residual correlations caused by the finite size of the model MT population from each bin in Figures 4B–4F. At the suggestion of an anonymous reviewer, we also demonstrate that the structure of MT-pursuit correlations in our data was reproduced by an optimal linear decoder that computes the weighted sum of the responses of a population of model MT neurons. For the same MT population responses used to create Figure 4, we computed the weight matrix W that provided the best prediction of target velocity (S’) through linear decoding: equation(Equation 10) S′=W×RS′=W×Rwhere R is a matrix of model neurons with different preferred speeds and directions. We then computed MT-pursuit correlations exactly as we did for our data, leading to the image in Figure 4G.