Extending GLASSO to non-Gaussian settings: sparse concentration estimation via EM algorithm

Abstract This paper develops graphical modeling techniques for multivariate non-Gaussian data, in which the sparsity pattern of the concentration matrix encodes conditional uncorrelations among variables. This structure enables efficient covariance selection, yielding concentration graph models that extend beyond the Gaussian case. Within elliptically symmetric distributions and indeed in an even broader family, distributions for which the best prediction is linear, zero partial correlations imply zero conditional correlations. That preserves the interpretability of edges in the graphical model. Focusing on elliptically symmetric families such as the generalized hyperbolic and power exponential distributions, we propose a modified graphical LASSO (GLASSO) framework for estimating sparse concentration matrices. The method is implemented using an EM-type algorithm adapted from Gaussian GLASSO to accommodate non-Gaussian likelihoods. Simulation studies and real-data applications demonstrate the effectiveness and robustness of the proposed estimators in recovering underlying graphical structures despite deviations from normality.