Title: An l0-constrained and l1-regularized estimator for graphical models Authors:  Alessandro Fulci - University of Trento (Italy)
Sandra Paterlini - University of Trento (Italy) [presenting]
Emanuele Taufer - University of Trento (Italy)
Abstract: Graphical models provide a versatile framework for representing conditional dependencies among random variables, with the precision matrix playing a central role in capturing these relationships. Traditional estimation methods, such as the Graphical Lasso (Glasso) with l1 regularization, suffer from key limitations, including significant bias, absence of grouping effects, and sensitivity to regularization parameters. On the other hand, algorithms leveraging l0 regularization can address some of these drawbacks but often lack shrinkage, leading to potential instability. To overcome these challenges, we introduce the Sparsity Constrained Graphical Lasso (SCGlasso), a novel estimator that integrates an l0 constraint on the number of non-zero elements with an l1 penalty. This hybrid approach decouples sparsity promotion from shrinkage, effectively addressing the limitations of l1 and l0 regularization in isolation. We design a coordinate descent algorithm for SCGlasso and establish its convergence to a local minimum. Through extensive simulations, we benchmark SCGlasso against established methods, including Glasso, Selo, and Atan penalties. The results highlight its superior performance in model selection accuracy and robustness, particularly in small sample scenarios. Finally, we demonstrate its practical utility through an application to gene expression data, showcasing the method's effectiveness in uncovering meaningful conditional dependency structures.