概率图模型及其独立性研究

发布时间：2018-06-10 04:27

本文选题：概率图模型 + 因子　；参考：《青岛大学》2017年硕士论文

【摘要】：概率图模型利用图形结构所隐含的结构特征,将概率分布变量间的关系给表示出来,不仅变得更加直观,同时也一定程度的简化了运算。由于这样的优势,概率图模型在不确定性推理中占据着重要的位置,并且在医疗诊断、人工智能、数据挖掘等方面有着很好的表现。对概率图模型的模型表示,以及相应的独立性知识进行研究,并讨论了分布和图之间的关系,给出几个新的算法。第一部分介绍了几个常用概率分布的表示,例如表格CPD、确定性CPD等离散节点变量的表示,高斯模型等连续节点变量的表示,以及混合模型。第二部分详细介绍了贝叶斯网络的模型表示,包括网络结构和独立性,其中一种特殊的贝叶斯网络—朴素贝叶斯网络,讨论了贝叶斯网络中分布和图之间的关系,给出一个分布已知的情况下利用次序关系构建网络结构图的算法,并且提供了一种利用父节点寻找最优次序关系的思路。第三部分介绍了马尔可夫网络的结构图以及参数化问题,而参数化的过程一般被认为是因子化的过程,于是给出了两个新的搜索算法,分别关于最大团和极大团,这为因子化做准备,然后讨论马尔可夫网络中的独立性,并说明它们之间的包含关系,同时介绍贝叶斯网络向马尔可夫网络的转化。最后对文章做出总结,同时对分布和图的转化、算法的改进以及两大网络间的转化等方面所面临的问题做了说明。
[Abstract]:The probabilistic graph model not only becomes more intuitive, but also simplifies the operation to a certain extent by using the implicit structural characteristics of the graph structure to express the relationship between the probability distribution variables. Because of this advantage, probabilistic graph model plays an important role in uncertain reasoning, and has a good performance in medical diagnosis, artificial intelligence, data mining and so on. The model representation of probabilistic graph model and the corresponding independence knowledge are studied. The relationship between distribution and graph is discussed and several new algorithms are given. The first part introduces the representation of several commonly used probability distributions, such as the representation of discrete node variables such as table CPD, deterministic CPDs, continuous node variables such as Gao Si model, and mixed models. In the second part, the model representation of Bayesian network is introduced in detail, including network structure and independence. A special Bayesian network-naive Bayesian network is introduced. The relationship between distribution and graph in Bayesian network is discussed. This paper presents an algorithm to construct the network structure diagram by using the order relation in the case of known distribution, and provides a way to find the optimal order relation by using the parent node. In the third part, we introduce the structure diagram and parameterization of Markov networks, and the parameterization process is generally considered as a factorization process. This is the preparation for factorization, then the independence of Markov networks is discussed, the inclusions between them are explained, and the transformation from Bayesian networks to Markov networks is also introduced. Finally, the paper summarizes the problems faced by the transformation of the distribution and graph, the improvement of the algorithm and the transformation between the two networks.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O21

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