Shared Information for a Markov Chain on a Tree
arXiv:2307.15844 · doi:10.1109/TIT.2024.3353769
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.
13 pages, 4 figures, submitted to IEEE Transactions on Information Theory