Contrastive Structured Anomaly Detection for Gaussian Graphical Models

by   Abhinav Maurya, et al.

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.


page 1

page 2

page 3

page 4


Learning Directed Graphical Models from Gaussian Data

In this paper, we introduce two new directed graphical models from Gauss...

Anomaly Detection via Graphical Lasso

Anomalies and outliers are common in real-world data, and they can arise...

Innovated scalable efficient estimation in ultra-large Gaussian graphical models

Large-scale precision matrix estimation is of fundamental importance yet...

Precision Matrix Estimation with Noisy and Missing Data

Estimating conditional dependence graphs and precision matrices are some...

Anomaly Detection and Localisation using Mixed Graphical Models

We propose a method that performs anomaly detection and localisation wit...

Robust Online Covariance and Sparse Precision Estimation Under Arbitrary Data Corruption

Gaussian graphical models are widely used to represent correlations amon...

Learning a Common Substructure of Multiple Graphical Gaussian Models

Properties of data are frequently seen to vary depending on the sampled ...

Please sign up or login with your details

Forgot password? Click here to reset