论文标题
关于马尔可夫随机字段的功能
On Functions of Markov Random Fields
论文作者
论文摘要
我们在给定图上的马尔可夫随机场（MRF）的函数得出了两个足够的条件，即在同一图上为MRF。第一个条件是信息理论，并与马尔可夫链块状的最新信息理论表征相似。第二个条件更容易检查，是基于相应Gibbs字段的潜在功能。我们在几个示例中说明了足够的条件，并讨论了对MRF的实际应用的影响。作为综上的结果，我们给出了信息提供信息的MRF功能的部分表征。
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.
