A Novel l0-Constrained Gaussian Graphical Model for Anomaly Localization

We consider the problem of anomaly localization in a sensor network for multivariate time-series data by computing anomaly scores for each variable separately. To estimate the sparse Gaussian graphical models (GGMs) learned from different sliding windows of the dataset, we propose a new model wherein we constrain sparsity directly through L0 constraint and apply an additional L2 regularization in the objective. We then introduce a proximal gradient algorithm to efficiently solve this difficult nonconvex problem. Numerical evidence is provided to show the benefits of using our model and method over the usual convex relaxations for learning sparse GGMs using a real dataset.