Shared Information -- New Insights and Problems in Decomposing Information in Complex Systems

Understand

How can the information that a set ${X_{1},...,X_{n}}$ of random variables contains about another random variable $S$ be decomposed? To what extent do different subgroups provide the same, i.e.

• shared or redundant, information, carry unique information or interact for the emergence of synergistic information? Recently Williams and Beer proposed such a decomposition based on natural properties for shared information.
• While these properties fix the structure of the decomposition, they do not uniquely specify the values of the different terms.
• Therefore, we investigate additional properties such as strong symmetry and left monotonicity.