贝叶斯网分解理论及其应用

项目名称： 贝叶斯网分解理论及其应用

项目编号： No.11726630

项目类型： 专项基金项目

立项/批准年度： 2018

项目学科： 数理科学和化学

项目作者： 孙毅

作者单位： 新疆大学

项目金额： 10万元

中文摘要： 随着计算机技术的飞速发展和人工智能、大数据等新兴战略产业的兴起，人们开始步入了海量信息的数据时代。因此，在进行数据分析和数据挖掘时，如何降低变量的维数和降低问题的复杂程度越来越成为一个非常现实、非常重要和非常迫切的问题。近些年，图模型的分解理论、可压缩理论以及结构学习理论在生物信息学、经济学、社会学、因果推断、人工智能和统计学等领域的成功应用为解决这些问题提供了非常有竞争力的途径。目前，有关无向图模型（又称马尔科夫网）的分解和可压缩性研究已经形成了比较系统完整的理论体系，但是有向无圈图模型（又称贝叶斯网）的分解理论还没有建立起来，而有关可压缩性的研究也只有初步的理论成果。因此，本项目将在统计学的应用背景下，基于贝叶斯网的有向分离准测，借助图论领域中的研究方法针对贝叶斯网的分解理论展开研究，同时将在分解理论的基础上进一步研究贝叶斯网的可压缩性和结构学习等问题。

中文关键词： 贝叶斯网；图模型；可压缩性；分解；d-分离准则

英文摘要： With the rapid development of computer technology and the spring of strategic industries such as artificial intelligence, big data and so on, we are stepping into an data times of mass information. As a result, how to reduce variable dimensions and the complexity of the problem has become a very practical, important and urgent probem when people carry on data analysis and data mining. In recent years, since the decomposition theory, collapsibility theory and structural learning theory of graphical models have successful applications to the fields of bio-informatics, economics, sociology, causal inference, artificial intelligence, statistics and so on, these methods provide very competitive ways to release these problems. Now studies on decomposition and collapsibility theory of undirected graphical models （also called Markov networks）have formed a relatively systematic and complete theoretical system. However, the decomposition theory of its counterpart called directed acyclic graphical models (also called Bayesian networks) has not been established, and only the related study of collapsibility theory has some rudimentary theoretical results. So, based on the d-separation criterion and the applied background of statistics, this project will conduct the research on the decomposition theory of Bayesian networks by using approaches and technologies in graph theory. In the mean time, we will study further the callpsibility and structural learning prblems in Bayesian networks on the basis of decomposition theory.

英文关键词： Bayesian networks;Graphical models;Collapsibility;Decomposition;d-separation criterion