论文标题
Markov连锁店的信息理论减少
Information-Theoretic Reduction of Markov Chains
论文作者
论文摘要
我们调查了减少马尔可夫连锁店的信息理论方法。我们的调查分为两个部分：第一部分考虑了马尔可夫链粗晶状，它的重点是将马尔可夫链投影到一个较小的状态空间上的过程中，该过程有一定含量的关注。第二部分考虑了马尔可夫链模型的减少，该模型的重点是用简化的模型代替原始的马尔可夫模型，该模型的行为与原始的马尔可夫模型相似。我们通过将无监督的机器学习问题作为马尔可夫链的减少问题来讨论在知识发现和数据挖掘领域的实际相关性。最后，我们简要讨论了块状性的概念，即当粗栅格产生降低的马尔可夫模型时，这种现象。
We survey information-theoretic approaches to the reduction of Markov chains. Our survey is structured in two parts: The first part considers Markov chain coarse graining, which focuses on projecting the Markov chain to a process on a smaller state space that is informative}about certain quantities of interest. The second part considers Markov chain model reduction, which focuses on replacing the original Markov model by a simplified one that yields similar behavior as the original Markov model. We discuss the practical relevance of both approaches in the field of knowledge discovery and data mining by formulating problems of unsupervised machine learning as reduction problems of Markov chains. Finally, we briefly discuss the concept of lumpability, the phenomenon when a coarse graining yields a reduced Markov model.
