  Recent studies invoke the superiority of the multivariate Total Correlation
concept over the conventional pairwise measures of functional connectivity in
biological networks. Those seminal works certainly show that empirical measures
of Total Correlation lead to connectivity patterns that differ from what is
obtained using the most popular measure, linear correlation, or its higher
order and nonlinear alternative Mutual Information. However, they do not
provide analytical results that explain the differences beyond the obvious
multivariate versus bivariate definitions. Moreover, the accuracy of the
empirical estimators could not be addressed directly because no controlled
scenario with known analytical result was provided either. This point is
critical because empirical estimation of information theory measures is always
challenging. As opposed to previous empirical approaches, in this work we
present analytical results to prove the advantages of Total Correlation over
Mutual Information to describe the functional connectivity. In particular, we
do it in neural networks for early vision (retina-LGN-cortex) which are
realistic but simple enough to get analytical results. The presented analytical
setting is also useful to check empirical estimates of Total Correlation.
Therefore, once certain estimate can be trusted, one can explore the behavior
with natural signals where the analytical results (that assume Gaussian
signals), may not be valid. In this regard, as applications (a) we explore the
effect of connectivity and feedback in the analytical retina-LGN-cortex network
with natural images, and (b) we assess the functional connectivity in visual
areas V1-V2-V3-V4 from actual fMRI recordings.
