[2202.05775] Inference of Multiscale Gaussian Graphical Model

Statistics > Machine Learning arXiv:2202.05775 (stat) [Submitted on 11 Feb 2022 (v1), last revised 23 Mar 2026 (this version, v3)] Title:Inference of Multiscale Gaussian Graphical Model Authors:Do Edmond Sanou, Christophe Ambroise, Geneviève Robin View a PDF of the paper titled Inference of Multiscale Gaussian Graphical Model, by Do Edmond Sanou and 1 other authors View PDF Abstract:Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering to reduce dimensionality and improve performances. This paper explores a slightly different paradigm where clustering is not knowledge-driven but performed simultaneously with the graph inference task. We introduce a novel Multiscale Graphical Lasso (MGLasso) to improve networks interpretability by proposing graphs at different granularity levels. The method estimates clusters through a convex clustering approach - a relaxation of k-means, and hierarchical clustering. The conditional independence graph is simultaneously inferred through a neighborhood selection scheme for undirected graphical models. MGLasso extends and generalizes the sparse group fused lasso problem to undirected graphical models. We use continuation with Nesterov smoothing in a shrinkage-thresholding algorithm (CONESTA) to propose a regularization path of solutions along the group fused Las...