Information Decomposition Based on Cooperative Game Theory

Nihat Ay, Daniel Polani, Nathaniel Virgo

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Abstract

We offer a new approach to the information decomposition problem in information theory: given a ‘target’ random variable co-distributed with multiple ‘source’ variables, how can we decompose the mutual information into a sum of non-negative terms that quantify the contributions of each random variable, not only individually but also in combination? We derive our composition from cooperative game theory. It can be seen as assigning a “fair share” of the mutual information to each combination of the source variables. Our decomposition is based on a different lattice from the usual ‘partial information decomposition’ (PID) approach, and as a consequence our decomposition has a smaller number of terms: it has analogs of the synergy and unique information terms, but lacks terms cor- responding to redundancy. Because of this, it is able to obey equivalents of the axioms known as ‘local positivity’ and ‘identity’, which cannot be simultaneously satisfied by a PID measure.
Original languageEnglish
Pages (from-to)979-1014
JournalKybernetika
Volume56
Issue number5
DOIs
Publication statusPublished - 5 Dec 2020

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