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Article overview
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Contrastive Structured Anomaly Detection for Gaussian Graphical Models | | Abhinav Maurya
; Mark Cheung
; | | Date: |
2 May 2016 | | Abstract: | Gaussian graphical models (GGMs) are probabilistic tools of choice for
analyzing conditional dependencies between variables in complex systems.
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 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 $l_1$ norm of difference between the
foreground precision being estimated and the already learned background
precision. We 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. | | Source: | arXiv, 1605.0355 | | Services: | Forum | Review | PDF | Favorites | |
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