Measure-Transformed Graphical Lasso

This paper tackles the problem of robust Gaussian graphical modeling in the presence of outliers. To this end, we propose a new robust variant of the GLASSO estimator, called measure-transformed (MT) GLASSO. This estimator operates by applying a transform to the probability measure of the data. The transform is generated by a non-negative data-weighting function, called MT-function. Specifically, we employ a Gaussian-Shaped MT-function, which effectively suppresses outliers and ensures transformation invariance of the nominal graph structure. Consequently, in MT-GLASSO, the standard sample covariance matrix is replaced with the empirical MT-covariance. The MT-GLASSO maintains the simplicity and computational efficiency of GLASSO. Furthermore, we propose a data-driven procedure to determine the scale parameter of the Gaussian MT-function, which controls the extent of outlier shrinkage. This procedure limits the Fisher-Information loss in the transform domain. The MT-GLASSO is illustrated in a simulation study highlighting its advantages over GLASSO and other robust extensions.