Contrastive Structured Anomaly Detection for Gaussian Graphical Models
Contrastive Structured Anomaly Detection for Gaussian Graphical Models
复制标题
高斯图模型的对比结构化异常检测
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Mark Cheung
中科院分区：
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作者：
Abhinav K. Maurya;Mark Cheung
高斯图形模型（GGM）是用于分析复杂网络系统（例如社交网络，传感器网络，金融市场等）变量之间有条件依赖性的概率工具。由GGM建模的基础系统。为了检测GGM中的结构异常，我们考虑了估计相应多元高斯分布的精确矩阵变化的问题。我们采用了两步方法来解决此问题： - （i）使用过去的系统观测值估算背景精度矩阵，而没有任何异常，并且（ii）在异常监测过程中使用滑动时间窗口估算前景精度矩阵。我们的主要贡献是使用新型的对比反向协方差估计程序估算前景精度。为了准确地了解GGM的结构变化，我们最大程度地提高了惩罚的对数类似性，即惩罚是估计的前景精度与已经学习过的背景精度之间的差异规范。我们适当地修改了乘数的交替方向方法（ADMM）算法，以进行稀疏的逆协方差估计，以执行前景精度矩阵的对比度估计。与非对抗性滑动窗口基线相比，我们对模拟GGM数据的结果显示了检测GGM结构变化的精度和回忆的显着提高。
Gaussian graphical models (GGMs) are probabilistic tools of choice for analyzing conditional dependencies between variables in complex networked systems such as social networks, sensor networks, financial markets, etc. Finding changepoints in the structural evolution of a GGM is therefore essential to detecting anomalies in the underlying system modeled by the GGM. In order to detect structural anomalies in a GGM, we consider the problem of estimating changes in the precision matrix of the corresponding multivariate Gaussian distribution. We take a two-step approach to solving this problem:- (i) estimating a background precision matrix using system observations from the past without any anomalies, and (ii) estimating a foreground precision matrix using a sliding temporal window during anomaly monitoring. Our primary contribution is in estimating the foreground precision using a novel contrastive inverse covariance estimation procedure. In order to accurately learn only the structural changes to the GGM, we maximize a penalized log-likelihood where the penalty is the l1 norm of difference between the foreground precision being estimated and the already learned background precision. We suitably modify the alternating direction method of multipliers (ADMM) algorithm for sparse inverse covariance estimation to perform contrastive estimation of the foreground precision matrix. Our results on simulated GGM data show significant improvement in precision and recall for detecting structural changes to the GGM, compared to a non-contrastive sliding window baseline.