Robust and Missing-Data-Aware Time-Varying Graphical Lasso(RM-TVGL) for High-Dimensional Dynamic Network Estimation

Time-varying graphical models provide a powerful framework for capturing the evolving conditional dependencies among high-dimensional variables over time. A widely used method in this context is the Time-Varying Graphical Lasso (TVGL), which estimates a sequence of sparse precision matrices while encouraging temporal smoothness. However, standard TVGL assumes Gaussian-distributed, fully observed data, making it vulnerable to outliers and missing values—common challenges in real-world applications. In this work, we introduce RM-TVGL: a Robust and Missing-Data-Aware Time-Varying Graphical Lasso framework that extends TVGL to accommodate noisy and incomplete data. Our method integrates Huber loss to mitigate the influence of outliers and incorporates an Expectation-Maximization (EM) algorithm to handle missing entries in a principled manner. Additionally, RM-TVGL supports flexible regularization schemes, including ℓ1, ℓ2, and Elastic Net, enabling adaptation to diverse network structures. We develop an efficient ADMMbased optimization algorithm and demonstrate the advantages of RM-TVGL through extensive experiments on both synthetic and real gene expression datasets. The results show that RMTVGL consistently improves structural accuracy, temporal stability, and robustness compared to existing methods.