Shared Information for a Markov Chain on a Tree
Information Theory
2024-01-23 v2 math.IT
Abstract
Shared information is a measure of mutual dependence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit characterization of shared information. The Markov chain on a tree is shown to possess a global Markov property based on graph separation; this property plays a key role in our proofs. When the underlying joint distribution is not known, we exploit the special form of this characterization to provide a multiarmed bandit algorithm for estimating shared information, and analyze its error performance.
Cite
@article{arxiv.2307.15844,
title = {Shared Information for a Markov Chain on a Tree},
author = {Sagnik Bhattacharya and Prakash Narayan},
journal= {arXiv preprint arXiv:2307.15844},
year = {2024}
}
Comments
13 pages, 4 figures, submitted to IEEE Transactions on Information Theory