An axiomatic characterization of mutual information

James Fullwood

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arXiv · 2108.12647

An axiomatic characterization of mutual information

James Fullwood

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Abstract

We characterize mutual information as the unique map on ordered pairs of random variables satisfying a set of axioms similar to those of Faddeev's characterization of the Shannon entropy. There is a new axiom in our characterization however which has no analogue for Shannon entropy, based on the notion of a Markov triangle, which may be thought of as a composition of communication channels for which conditional entropy acts functorially. Our proofs are coordinate-free in the sense that no logarithms appear in our calculations.

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James Fullwood. 2021-08-28. An axiomatic characterization of mutual information. https://arxiv.org/abs/2108.12647

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