Network information and connected correlations.
Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible N-point correlation is measured by a decrease in entropy for the joint distribution of N variables relative to the maximum entropy allowed by all the observed N-1 variable distributions. We calculate the "connected information" terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.
Schneidman
Elad
E
Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Still
Susanne
S
Berry
Michael J
MJ
Bialek
William
W
D007255:Information Services; D008957:Models, Genetic; D008959:Models, Neurological; D008962:Models, Theoretical