Assuming that the population response follows a multivariate normal distribution , the conditional dependencies between pairs of neurons are expressed by the partial correlations between them.

We evaluated the covariance matriX estimators using a loss function derived from the normal distribution .

However, this does not limit the applicability of its conclusions to normal distributions .

Here, in the role of the loss function we adopted the Kullback-Leibler divergence between multivariate normal distributions with equal means, scaled by; to make its values comparable across different population sizes:

For simulation, ground truth covariance matrices were produced by taking 150 independent samples from an artificial population of 50 independent, identically normally distributed units.

Samples were then drawn from multivariate normal distributions models with the respective true covariance matrices to be estimated by each of the estimators.

As discussed in Methods, we attributed tomographic density to each of the 25 long edges of the polyhedral cage representing the icosahedrally-averaged density considered in this analysis and fitted it to a normal distribution .

A ranking of the level of density associated with these edges was achieved using the mean of the fitted normal distribution .

We computed fitted normal distributions using the normfit function from the scipy.stats python library, since for a sparse dataset the mean of a fitted normal distribution is less affected by outliers than the raw data.

The normal fitting function automatically calculated the best positioning of a unimodal normal distribution for the dataset.

Then, § (given 5) is normally distributed , and eq.

We obtain them as the best (MSE) fit to the following formula: where (I) is the standard cumulative normal distribution .

(Actually, we postulate that E[PlK] is exactly diagonal when the random vectors x.- follow a normal distribution .