Responses of single neurons to a fixed stimulus are usually both variable and highly ambiguous. Therefore, it is widely assumed that stimulus parameters are encoded by populations of neurons. An important aspect in population coding that has received much interest in the past is the effect of correlated noise on the accuracy of the neural code.
Theoretical studies have investigated the effects of different correlation structures on the amount of information that can be encoded by a population of neurons based on Fisher Information. Unfortunately, to be analytically tractable, these studies usually have to make certain simplifying assumptions such as high firing rates and Gaussian noise. Therefore, it remains open if these results also hold in the more realistic scenario of low firing rates and discrete, Poisson-distributed spike counts.
In order to address this question we have developed a straightforward and efficient method to draw samples from a multivariate near-maximum entropy Poisson distribution with arbitrary mean and covariance matrix based on the dichotomized Gaussian distribution . The ability to extensively sample data from this class of distributions enables us to study the effects of different types of correlation structures and tuning functions on the information encoded by populations of neurons under more realistic assumptions than analytically tractable methods.
Specifically, we studied how limited range correlations (neurons with similar tuning functions and low spatial distance are more correlated than others) affect the accuracy of a downstream decoder compared to uniform correlations (correlations between neurons are independent of their properties and locations). Using a set of neurons with equally spaced orientation tuning functions, we computed the error of an optimal linear estimator (OLE) reconstructing stimulus orientation from the neurons’ firing rates. We find—supporting previous theoretical results—that irrespective of tuning width and the number of neurons in the network, limited range correlations decrease decoding accuracy while uniform correlations facilitate accurate decoding. The optimal tuning width, however, did not change as a function of either the correlation structure or the number of neurons in the network. These results are particularly interesting since a number of experimental studies report limited range correlation structures (starting at around 0.1 to 0.2 for similar neurons) while experiments carried out in our own lab suggest that correlations are generally low (on the order of 0.01) and uniform.
 P. Berens and M. Bethge, NCCD (2007).