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September 24, 2025Open Access

Identifying Network Hubs with the Partial Correlation Graphical LASSO

MBMałgorzata BogdanWrocław University of Science and Technology ACAdam ChojeckiWarsaw University of Technology IHIvan HejnýLund University

Key Points

PCGLASSO enhances network analysis by providing consistent model selection through a novel scale-invariant method.
It introduces a weaker irrepresentability criterion than the standard graphical lasso, boosting empirical performance.
The theoretical framework includes the first analysis of the estimator's non-convex solution landscape for global uniqueness.
These findings suggest that PCGLASSO could significantly improve the recovery of network structures with hubs.

Abstract

The Partial Correlation Graphical LASSO (PCGLASSO) offers a scale-invariant alternative to the standard GLASSO. This paper provides the first comprehensive treatment of the PCGLASSO estimator. We introduce a novel and highly efficient algorithm. Our central theoretical contribution is the first scale-invariant irrepresentability criterion for PCGLASSO, which guarantees consistent model selection. We prove this condition is significantly weaker than its GLASSO counterpart, providing the first theoretical justification for PCGLASSO's superior empirical performance, especially in recovering networks with hub structures. Furthermore, we deliver the first analysis of the estimator's non-convex solution landscape, establishing new conditions for global uniqueness and guaranteeing the consistency of all minimizers.

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