An axiomatic characterization of mutual information
Information Theory
2022-11-30 v2 math.IT
Probability
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.
Keywords
Cite
@article{arxiv.2108.12647,
title = {An axiomatic characterization of mutual information},
author = {James Fullwood},
journal= {arXiv preprint arXiv:2108.12647},
year = {2022}
}
Comments
No figures, no logarithms