高斯图模型的基于联接树改进的IPSP算法  

An Improved IPSP Procedure Using Junction Tree for Gaussian Graphical Models

作　　者：孙聚波 徐平峰 单娜 邓文礼 SUN Jubo;XU Pingfeng;SHAN Na;DENG Wenli(School of Applied Sciences,Jilin Engineering Normal University,Changchun,130052,China;Department of Statistics,Changchun University of Technology,Changchun,130012,China;School of Psychology,Northeast Normal University,Changchun,130024,China;Department of Mathematics and Statistics,Hang Seng Management College,Hong Kong)

机构地区：[1]吉林工程技术师范学院应用理学院,长春130052 [2]长春工业大学统计系,长春130012 [3]东北师范大学心理学院,长春130024 [4]恒生管理学院数学及统计学系

出　　处：《应用概率统计》2018年第3期319-330,共12页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11571050;11701043);吉林省教育厅项目(批准号:2016315);香港研究资助局项目(批准号:UGC/FDS14/P01/16)资助

摘　　要：IPSP算法是求解高斯图模型中参数极大似然估计的一种高效算法.它先将图模型的团边缘分伙,而后局部调整每伙内的团边缘.本文利用联接树上的IIPS算法,替代IPSP算法每伙内的局部调整,提出了新算法IPSP-JT以降低IPSP的复杂度.并且我们给出了进行局部调整时IIPS所使用的边数最少的图结构,证明了其存在唯一性,同时构建了局部的联接树.数值模拟显示,对于高维高斯图模型,IPSP-JT算法比IPSP算法速度更快.The IPSP algorithm is an efficient algorithm for computing maximum likelihood estimation of Gaussian graphical models.It rst divides clique marginals of graphical models into several groups,and then it adjusts clique marginals in each group locally.This paper uses the IIPS algorithm on junction tree to replace local adjustment on each group in the IPSP algorithm and propose a resulting algorithm called IPSP-JT to reduce the complexity of the IPSP algorithm.Moreover,we give a graph with minimum edges used by IIPS to adjust locally,and we prove its existence and uniqueness and construct a local junction tree.Numerical experiments show that the IPSP-JT algorithm runs faster than the IPSP algorithm for large Gaussian graphical models.

关 键 词：迭代比例拟合算法 马氏性 三角化图 传交性 联按树 

分 类 号：O212.4[理学—概率论与数理统计]