Convergence-Guaranteed Elastic Net Graphical Model Estimation with Applications to Anomaly Localization

Estimating dependency structures from noisy multivariate variables is fundamentally important in many applications. Of particular importance in practice is anomaly localization, which is to compute a variable-wise anomaly score by comparing a target dependency structure to a reference structure. In this task, stably and accurately estimating the dependency structures is the key. First, we present an $l_0-elastic$ net model for estimating sparse inverse covariance matrices. Then we introduce a framework for anomaly localization that utilizes both the $l_0-elastic$ net model and a transfer learning model. Although $l_0$- constrained optimization is known to be challenging, we introduce a hard thresholding line-search algorithm to efficiently solve these graphical models. Using synthetic and real-world data sets, we demonstrate that the proposed $l_0$-based method systematically outperforms alternative methods in many use-cases.