Multivariate Mutual Information Inspired by Secret-Key Agreement This paper motivates the multiterminal secret-key capacity as a useful measure of multivariate mutual information, develops information-theoretic properties of this measure, and makes comparisons with other existing multivariate correlation measures.

The capacity for multiterminal secret-key agree- ment inspires a natural generalization of Shannon's mutual information from two random variables to multiple random variables. Under a general source model without helpers, the capacity is shown to be equal to the normalized divergence from the joint distribution of the random sources to the product of marginal distributions minimized over partitions of the random sources. The mathematical underpinnings are the works on co-intersecting submodular functions and the prin- ciple lattices of partitions of the Dilworth truncation. We clarify the connection to these works and enrich them with informa- tion-theoretic interpretations and properties that are useful in solving other related problems in information theory as well as machine learning.