Unique Informations and Deficiencies

Abstract

Given two channels that convey information about the same random variable, we introduce two measures of the unique information of one channel with respect to the other. The two quantities are based on the notion of generalized weighted Le Cam deficiencies and differ on whether one channel can approximate the other by a randomization at either its input or output. We relate the proposed quantities to an existing measure of unique information which we call the minimum-synergy unique information. We give an operational interpretation of the latter in terms of an upper bound on the one-way secret key rate and discuss the role of the unique informations in the context of nonnegative mutual information decompositions into unique, redundant and synergistic components.

13 pages, 2 figures. The material in this manuscript was presented at the 56th Annual Allerton Conference on Communication, Control, and Computing, 2018. This manuscript contains some corrections: most notably, Lemma 18 was removed and Proposition 28 was corrected. The numbering of equations and results in this version agrees with the numbering of the published version

References in corpus (3)

• Secret Sharing and Shared Information
• Reconsidering unique information: Towards a multivariate information decomposition
• Computing the Unique Information

Cited by in corpus (6)

• A Novel Approach to the Partial Information Decomposition
• Unique Information and Secret Key Agreement
• Partial Information Decomposition via Deficiency for Multivariate Gaussians
• Unique Information and Secret Key Decompositions
• The Variational Deficiency Bottleneck
• Partial information decomposition: redundancy as information bottleneck