Common Informations

These measures all somehow measure shared information, but do not equal the mutual information in the bivariate case. All of them are importable from dit.multivariate.

• Gács-Körner Common Information
• Wyner Common Information
• Channel Synthesis
• Exact Common Information
• Functional Common Information
• Kamath-Anantharam Common Information
• Maximum Entropy Function
• MSS Common Information
• Beta Common Information
• Stochastic Gács–Körner Common Information
• Tension Common Information

The directed Kamath–Anantharam quantity directed_kamath_common_information() is documented on the Kamath-Anantharam Common Information page.

Several of these quantities are corner points of the Gray–Wyner region; see The Gray-Wyner Network for the operational picture.

Ordering

The common information measures (together with the Dual Total Correlation and CAEKL Mutual Information) form an ordering:

\[\K{X_{0:n}} \leq \J{X_{0:n}} \leq \B{X_{0:n}} \leq \C{X_{0:n}} \leq \G{X_{0:n}} \leq \F{X_{0:n}} \leq U(X_{0:n}) \leq \M{X_{0:n}}\]