一种基于改进Bhattacharyya距离的高斯网络协方差矩阵灵敏度分析方法  

An improved Bhattacharyya divergence for sensitivity analysis of covariance matrices in Gaussian Bayesian networks

作　　者：朱明敏 刘三阳 ZHU Mingmin;LIU Sanyang(School of Mathematics and Statistics,Xidian University,Xi'an 710126,China)

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710126

出　　处：《浙江大学学报（理学版）》2019年第1期9-14,21,共7页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(61877046);陕西省自然科学基础研究计划项目(2017JM1001);中央高校基本科研业务费项目(JBX180704)

摘　　要：提出了一种改进的Bhattacharyya距离,用以度量2个协方差矩阵之间的差异性,简称为SΣ距离。证明了该距离在正定矩阵空间中满足距离的3条性质:正定性、对称性以及三角不等性,并将SΣ距离用于高斯网络协方差矩阵的灵敏度分析。数值实验结果表明,利用SΣ距离得到的分析结果与KL距离、Bhattacharyya距离完全一致,由于SΣ距离满足三角不等性,大大降低了矩阵的运算量。In this work,we propose a divergence measure between two Gaussian covariance matrices,the SΣdivergence,which allows one to evaluate the global effects of small and large changes in the network parameters.We discuss some theoretical properties of SΣdivergence,including the positive definiteness,symmetry,triangular inequality constraints and show that it is a metric in the space of positive definite matrices.Then,we apply it to the task of sensitivity analysis in Gaussian Bayesian networks.The results obtained by SΣdivergence are almost completely consistent with those obtained by the KL and Bhattacharyya divergences,but the amount of computation is reduced greatly.

关 键 词：高斯贝叶斯网络 协方差矩阵 灵敏度分析 SΣ距离 

分 类 号：TP399[自动化与计算机技术—计算机应用技术]