A Perspective on Unique Information
Directionality, Intuitions, and Secret Key Agreement

Ryan G. James, Jeffrey Emenheiser, and James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

ABSTRACT: Recently, the partial information decomposition emerged as a promising framework for identifying the meaningful components of the information contained in a joint distribution. Its adoption and practical application, however, have been stymied by the lack of a generally-accepted method of quantifying its components. Here, we briefly discuss the bivariate (two-source) partial information decomposition and two implicitly directional interpretations used to intuitively motivate alternative component definitions. Drawing parallels with secret key agreement rates from information-theoretic cryptography, we demonstrate that these intuitions are mutually incompatible and suggest that this underlies the persistence of competing definitions and interpretations. Having highlighted this hitherto unacknowledged issue, we outline several possible solutions.


Ryan G. James, Jeffrey Emenheiser, and James P. Crutchfield, “A Perspective on Unique Information: Directionality, Intuitions, and Secret Key Agreement”, (2018).
doi:XXXX/XXXXXX.
[pdf]

arxiv.org:1808.08606.