Sledge Isaac J, Príncipe José C
Advanced Signal Processing and Automated Target Recognition Branch, US Naval Surface Warfare Center-Panama City Division, Panama City, FL 32407, USA.
Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA.
Entropy (Basel). 2019 Mar 30;21(4):349. doi: 10.3390/e21040349.
In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces, which is done via the negative, modified Kullback-Leibler divergence defined on a model joint space. Model reduction is achieved by solving a value-of-information criterion with respect to this divergence. Optimizing the criterion leads to a probabilistic partitioning of the states in the high-order Markov chain. A single free parameter that emerges through the optimization process dictates both the partition uncertainty and the number of state groups. We provide a data-driven means of choosing the 'optimal' value of this free parameter, which sidesteps needing to a priori know the number of state groups in an arbitrary chain.
在本文中，我们提出了一种获取马尔可夫链降阶模型的方法。我们的方法由两个信息论过程组成。第一个过程是一种比较不同状态空间上的平稳链对的方法，这是通过在模型联合空间上定义的负的、修正的库尔贝克-莱布勒散度来完成的。通过求解关于这种散度的信息价值准则来实现模型降阶。对该准则进行优化会导致高阶马尔可夫链中状态的概率划分。在优化过程中出现的单个自由参数决定了划分的不确定性和状态组的数量。我们提供了一种数据驱动的方法来选择这个自由参数的“最优”值，从而避免了事先需要知道任意链中状态组数量的问题。
