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Open AccessArticle

Generalised Measures of Multivariate Information Content

by Conor Finn 1,2,* and Joseph T. Lizier 1
1
Centre for Complex Systems, The University of Sydney, NSW 2006, Australia
2
CSIRO Data61, Marsfield NSW 2122, Australia
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(2), 216; https://doi.org/10.3390/e22020216
Received: 11 December 2019 / Revised: 5 February 2020 / Accepted: 12 February 2020 / Published: 14 February 2020
(This article belongs to the Section Information Theory, Probability and Statistics)
The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of multivariate information content that can be accurately depicted using Venn diagrams for any number of random variables. These measures complement the existing measures of multivariate mutual information and are constructed by considering the algebraic structure of information sharing. It is shown that the distinct ways in which a set of marginal observers can share their information with a non-observing third party corresponds to the elements of a free distributive lattice. The redundancy lattice from partial information decomposition is then subsequently and independently derived by combining the algebraic structures of joint and shared information content.
Keywords: information content; multivariate mutual information; information measures; information decomposition; synergy; redundancy information content; multivariate mutual information; information measures; information decomposition; synergy; redundancy
MDPI and ACS Style

Finn, C.; Lizier, J.T. Generalised Measures of Multivariate Information Content. Entropy 2020, 22, 216.

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