Title: Recovering network hubs with PCGLASSO: Theory, algorithm, and performance Authors:  Malgorzata Bogdan - University of Wroclaw (Poland) [presenting]
Adam Chojecki - Warsaw University of Technology (Poland)
Ivan Hejny - Lund University (Sweden)
Bartosz Kolodziejek - Politechnika Warszawska (Poland)
Jonas Wallin - Lund University (Sweden)
Abstract: Regularization techniques have become standard tools for estimating high-dimensional precision matrices and graphical models. These methods typically penalize the magnitudes of the elements in the precision matrix, which leads to a lack of scale invariance. This means that the structure of the estimated graphical model may change depending on how the variables are scaled. To overcome this limitation, the Partial Correlation LASSO (PCGLASSO) has been recently proposed. This method applies regularization directly to the elements of the partial correlation matrix. We will introduce a novel algorithm for PCGLASSO that is substantially more efficient than existing approaches. We will also present new theoretical results addressing convexity and consistency, including Irrepresentability Conditions for accurate graph structure recovery. Our theoretical insights, supported by empirical evidence, show that PCGLASSO significantly outperforms GLASSO, particularly in identifying key hub structures within the network.