马尔可夫链集结时状态数自动确定的信息论方法
An Information-Theoretic Approach for Automatically Determining the Number of States when Aggregating Markov Chains
摘要：
聚合马尔可夫链时的一个基本问题是状态组的数量的规范。太少的状态组可能无法充分捕获原始高阶马尔可夫链的相关动态。太多的状态组可能会导致一个非简约的，降阶马尔可夫链的复杂性的竞争对手的原始。在本文中，我们表明，一个增强的价值的信息为基础的方法，以聚集马尔可夫链，便于确定的状态组的数量。最佳状态组计数与降阶链的复杂性与原始和降阶链动态之间的相互依赖性相平衡的情况相吻合。
英文摘要：
A fundamental problem when aggregating Markov chains is the specification of the number of state groups. Too few state groups may fail to sufficiently capture the pertinent dynamics of the original, high-order Markov chain. Too many state groups may lead to a non-parsimonious, reduced-order Markov chain whose complexity rivals that of the original. In this paper, we show that an augmented value-of-information-based approach to aggregating Markov chains facilitates the determination of the number of state groups. The optimal state-group count coincides with the case where the complexity of the reduced-order chain is balanced against the mutual dependence between the original- and reduced-order chain dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
