A Bivariate Measure of Redundant Information

TL;DR

This paper introduces a new measure of redundant information between variables based on probability distribution projections, enabling better decomposition of mutual information into redundant and synergistic parts.

Contribution

It formalizes a novel measure of redundant information that satisfies key properties and improves upon previous measures, with applications to transfer entropy analysis.

Findings

The new measure satisfies all desired properties of redundancy.

It outperforms previous measures in example comparisons.

It effectively decomposes transfer entropy into redundant and synergistic components.

Abstract

We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual information, redundant information denotes information that is shared about the outcome of a third variable. Formalizing this concept, and being able to measure it, is required for the non-negative decomposition of mutual information into redundant and synergistic information. Previous attempts to formalize redundant or synergistic information struggle to capture some desired properties. We introduce a new formalism for redundant information and prove that it satisfies all the properties necessary outlined in earlier work, as well as an additional criterion that we propose to be necessary to capture redundancy. We also demonstrate the behaviour of this new measure for several examples, compare it to previous measures and apply it to the decomposition of transfer entropy.