Graphical LASSO for Estimating Associations in Elliptically Symmetric Distributions: An EM-Based Approach
A. B. A. Dawod${}^a$ and Gy. Terdik${}^b$
${}^a$Doctoral School of Informatics, University of Debrecen,
${}^b$Department of Information Technology, University of Debrecen
Modern data science applications frequently involve high-dimensional data that violates Gaussian assumptions. By encoding conditional dependencies within graphical models, concentration matrices enable interpretable statistical learning and exploratory data analysis.

This study develops a graphical modeling framework for non-Gaussian data based on elliptically symmetric and linear-predictor models. Within these families, zero partial correlations imply zero conditional correlations, ensuring that graph edges retain their interpretation as conditionally uncorrelated relationships. We therefore propose a modified GLASSO approach for estimating sparse concentration matrices for the generalized hyperbolic and power exponential families. By adapting an EM-type algorithm, the method enables efficient and scalable estimation in high-dimensional settings [1]. The proposed method is evaluated using simulation studies and real-data applications to assess its ability to recover underlying graphical structures under departures from normality. The results indicate that the modified framework provides improved robustness while maintaining accurate structure recovery in heavy-tailed and non-Gaussian settings [2].

Overall, this work contributes to the development of robust graphical modeling tools for modern data science, bridging statistical methodology and computational implementation.

Keywords: GLASSO, Elliptical distributions, EM algorithm.