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

TL;DR

This paper examines the challenges in quantifying components of partial information decomposition, highlighting incompatible intuitions and proposing potential solutions to unify the framework.

Contribution

It identifies fundamental incompatibilities in existing interpretations of partial information decomposition and suggests avenues for resolving these issues.

Findings

Incompatibility between directional intuitions and secret key agreement rates.

Highlighting the lack of a universally accepted method for quantifying information components.

Proposing possible solutions to unify the partial information decomposition framework.

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.