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.

翻译：共享信息是度量有限字母表上多个联合分布随机变量间相互依赖关系的一种测度。针对给定联合分布的树状马尔可夫链，我们给出了共享信息显式刻画的另一种证明。研究表明，基于图分离性质的树状马尔可夫链具有全局马尔可夫性——这一性质在证明中起关键作用。当底层联合分布未知时，我们利用该刻画的特殊形式，提出了一种用于估计共享信息的多臂老虎机算法，并分析了其误差性能。