title: Network information and connected correlations.
abstract: 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.
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Elad
authors.initials: E
authors.lastname: Schneidman
authors.forename: Susanne
authors.initials: S
authors.lastname: Still
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Berry
authors.forename: William
authors.initials: W
authors.lastname: Bialek
mesh_terms: D007255:Information Services; D008957:Models, Genetic; D008959:Models, Neurological; D008962:Models, Theoretical