Identifying Network Hubs with the Partial Correlation Graphical LASSO
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913103318351872 |
|---|---|
| author | Bogdan, Małgorzata Chojecki, Adam Hejný, Ivan Kołodziejek, Bartosz Wallin, Jonas |
| author_facet | Bogdan, Małgorzata Chojecki, Adam Hejný, Ivan Kołodziejek, Bartosz Wallin, Jonas |
| contents | Graphical LASSO (GLASSO) is a widely used method for estimating sparse precision matrices and learning undirected graphical models in high-dimensional settings. Because GLASSO penalizes entries of the precision matrix directly, however, it is not scale-invariant. Partial Correlation Graphical LASSO (PCGLASSO), introduced by Carter et al. (2024), addresses this limitation by penalizing partial correlations, which directly characterize conditional dependence. In this paper, we study both statistical and computational properties of the PCGLASSO estimator. Our main contribution is the introduction of a scale-invariant irrepresentability condition for PCGLASSO and the proof that this condition is sufficient for consistent model selection. We further show that this condition is weaker than the corresponding irrepresentability condition for GLASSO, helping to explain the improved empirical behavior of PCGLASSO in settings such as hub-structured graphs. In addition, we develop two efficient algorithms for computing the estimator and analyze the nonconvex optimization problem underlying PCGLASSO, deriving conditions for global uniqueness and showing consistency of all minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identifying Network Hubs with the Partial Correlation Graphical LASSO Bogdan, Małgorzata Chojecki, Adam Hejný, Ivan Kołodziejek, Bartosz Wallin, Jonas Statistics Theory Optimization and Control Primary 62H22, secondary 62H12, 62J07, 90C26 Graphical LASSO (GLASSO) is a widely used method for estimating sparse precision matrices and learning undirected graphical models in high-dimensional settings. Because GLASSO penalizes entries of the precision matrix directly, however, it is not scale-invariant. Partial Correlation Graphical LASSO (PCGLASSO), introduced by Carter et al. (2024), addresses this limitation by penalizing partial correlations, which directly characterize conditional dependence. In this paper, we study both statistical and computational properties of the PCGLASSO estimator. Our main contribution is the introduction of a scale-invariant irrepresentability condition for PCGLASSO and the proof that this condition is sufficient for consistent model selection. We further show that this condition is weaker than the corresponding irrepresentability condition for GLASSO, helping to explain the improved empirical behavior of PCGLASSO in settings such as hub-structured graphs. In addition, we develop two efficient algorithms for computing the estimator and analyze the nonconvex optimization problem underlying PCGLASSO, deriving conditions for global uniqueness and showing consistency of all minimizers. |
| title | Identifying Network Hubs with the Partial Correlation Graphical LASSO |
| topic | Statistics Theory Optimization and Control Primary 62H22, secondary 62H12, 62J07, 90C26 |
| url | https://arxiv.org/abs/2508.12258 |