概率图模型表示理论  

Representation Theory of Probabilistic Graphical Models

作　　者：刘建伟[1] 黎海恩 罗雄麟[1] 

机构地区：[1]中国石油大学(北京)自动化研究所,北京102249

出　　处：《计算机科学》2014年第9期1-17,共17页Computer Science

基　　金：国家重点基础研究发展计划项目(973计划)(2012CB720500);国家自然科学基金项目(21006127);中国石油大学(北京)基础学科研究基金项目(JCXK-2011-07)资助

摘　　要：概率图模型结合概率论与图论的知识,利用图来表示与模型有关的变量的联合概率分布。近年它已成为不确定性推理的研究热点,在人工智能、机器学习和计算机视觉等领域有广阔的应用前景。主要研究概率图模型的表示方法,讨论如何利用概率网络中的独立性来简化联合概率分布的方法表示。首先介绍了单个节点上的条件概率分布的表示模型及其引起的独立性,包括表格CPD、确定性CPD、特定上下文CPD、因果影响CPD、高斯模型和混合模型,并把单个分布模型推广到指数分布族中。然后详细介绍贝叶斯网络中的独立性以及图与概率分布的关系,讨论了高斯分布和指数分布族的贝叶斯网络表示理论。再详细描述马尔可夫网络的参数化问题及其独立性,也讨论高斯分布和指数分布族的马尔可夫网络表示理论。还给出两种局部有向图模型:条件随机场和链图。并且描述基于模板的概率模型表示,包括动态贝叶斯网络和状态观测模型这两种暂态模型,以及盘模型和概率关系模型这两种对象关系领域的有向概率模型,而且给出对象关系领域的无向表示。最后对概率图模型表示理论和方法所面临的问题及前景进行展望。Probabilistic graphical models bring together graph theory and probability theory in a formalism, so the joint probabilistic distribution of variables in the model can be represented using graph. In recent years, probabilistic graphical models have become the focus of the research in uncertainty inference, because of its bright prospect for the application in artificial intelligence, machine learning, computer vision and so on. This work introduced the representations of probabilistic graphical models and discussed how to represent the joint probabilistic distribution compactly using the independences in the network. First,models of the conditional probabilistic distribution of single node and their independences were introduced, including tabular CPD, deterministic CPD, context-specific CPD, CPD of causal influence, Gaussian models and hybrid models, and a general framework called the exponential family that encompasses a broad range of distributions was defined. Then Bayesian network representation and its independence properties were described in detail, as well as the Bayesian network of Gaussian distribution and exponential family. This work also introduced Markov network representation,independence properties in Markov network and Markov network of Gaussian distribution and exponential family. We also gave two partially directed models, conditional random fields and chain graph models. In addition,this work discussed template-based representations, including temporal models that contain dynamic Bayesian network and state-observation models, directed probabilistic models for object-relational domains which contain plate models and probabilistic relational models, and undirected representation for object-relational domains. Finally, this work raised some questions that probabilistic graphical models face with and discussed its development in the future.

关 键 词：概率图模型 贝叶斯网络 马尔可夫网络 动态贝叶斯网络 概率关系模型 条件随机场 链图 指数分布族 局部概率模型 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]