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

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S_Σ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S_Σ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S_Σ距离得到的分析结果与KL距离、Bhattacharyya距离完全一致，由于S_Σ距离满足三角不等性，大大降低了矩阵的运算量。

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

In this work, we propose a divergence measure between two Gaussian covariance matrices, the S_Σ divergence, which allows one to evaluate the global effects of small and large changes in the network parameters. We discuss some theoretical properties of S_Σ divergence, 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 S_Σ divergence are almost completely consistent with those obtained by the KL and Bhattacharyya divergences, but the amount of computation is reduced greatly.