Contrastive Structured Anomaly Detection for Gaussian Graphical Models

TL;DR

This paper introduces a contrastive inverse covariance estimation method to detect structural anomalies in Gaussian graphical models by comparing foreground and background precision matrices, improving change detection accuracy.

Contribution

The paper proposes a novel contrastive estimation procedure for the precision matrix in GGMs, enhancing anomaly detection by focusing on structural changes.

Findings

Significant improvement in precision and recall over baseline methods

Effective detection of structural changes in simulated GGM data

Modified ADMM algorithm for contrastive sparse inverse covariance estimation

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.