[2407.00644] Clusterpath Gaussian Graphical Modeling

Statistics > Machine Learning arXiv:2407.00644 (stat) [Submitted on 30 Jun 2024 (v1), last revised 24 Mar 2026 (this version, v3)] Title:Clusterpath Gaussian Graphical Modeling Authors:D. J. W. Touw, A. Alfons, P. J. F. Groenen, I. Wilms View a PDF of the paper titled Clusterpath Gaussian Graphical Modeling, by D. J. W. Touw and 3 other authors View PDF HTML (experimental) Abstract:Graphical models serve as effective tools for visualizing conditional dependencies between variables. However, as the number of variables grows, interpretation becomes increasingly difficult, and estimation uncertainty increases due to the large number of parameters relative to the number of observations. To address these challenges, we introduce the Clusterpath estimator of the Gaussian Graphical Model (CGGM) that encourages variable clustering in the graphical model in a data-driven way. Through the use of an aggregation penalty, we group variables together, which in turn results in a block-structured precision matrix whose block structure remains preserved in the covariance matrix. The CGGM estimator is formulated as the solution to a convex optimization problem, making it easy to incorporate other popular penalization schemes which we illustrate through the combination of an aggregation and sparsity penalty. We present a computationally efficient implementation of the CGGM estimator by using a cyclic block coordinate descent algorithm. In simulations, we show that CGGM not only matches, but ...