论文标题
隐藏马尔可夫进程的香农熵率
Shannon Entropy Rate of Hidden Markov Processes
论文作者
论文摘要
隐藏的马尔可夫连锁店是随机过程的广泛应用的统计模型，从基本物理和化学到金融，健康和人工智能。他们产生的隐藏的马尔可夫过程众所周知，即使链条是有限的状态也很复杂：由于其预测特征的集合通常是无限的，因此没有针对香农熵率的有限表达。因此，迄今为止，人们无法对它们的随机程度或结构化。在这里，我们通过展示如何有效，准确地计算其熵率来解决这一挑战的第一部分。我们还展示了该方法如何提供最小的无限预测特征。续集解决了挑战在结构上的第二部分。
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously complicated, however, even if the chain is finite state: no finite expression for their Shannon entropy rate exists, as the set of their predictive features is generically infinite. As such, to date one cannot make general statements about how random they are nor how structured. Here, we address the first part of this challenge by showing how to efficiently and accurately calculate their entropy rates. We also show how this method gives the minimal set of infinite predictive features. A sequel addresses the challenge's second part on structure.
