关于马尔可夫随机场的函数（CS IT）---蔡秋纯

我们得到了给定图上的马尔可夫随机场（MRF）函数是同一图上的MRF的两个充分条件。第一个条件是信息论，并与最近关于马尔可夫链集总性的信息论特征相比较。第二个条件，更容易检查，是基于相应的吉布斯场的势函数。我们用几个例子说明了我们的充分条件，并讨论了MRFs在实际应用中的意义。作为一个副结果，我们给出了磁流变液保持信息功能的部分特征。

原文标题：On Functions of Markov Random Fields

原文：We derive two sufficient conditions for a function of a Markov random field (MRF) on a given graph to be a MRF on the same graph. The first condition is information-theoretic and parallels a recent information-theoretic characterization of lumpability of Markov chains. The second condition, which is easier to check, is based on the potential functions of the corresponding Gibbs field. We illustrate our sufficient conditions at the hand of several examples and discuss implications for practical applications of MRFs. As a side result, we give a partial characterization of functions of MRFs that are information-preserving.

原文作者：Bernhard C. Geiger, Ali Al-Bashabsheh

原文地址：https://arxiv.org/abs/2005.13908