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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2308.08852 |
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| _version_ | 1866910925055852544 |
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| author | Wang, Chengjing Tang, Peipei He, Wenling Lin, Meixia |
| author_facet | Wang, Chengjing Tang, Peipei He, Wenling Lin, Meixia |
| contents | Graphical models have exhibited their performance in numerous tasks ranging from biological analysis to recommender systems. However, graphical models with hub nodes are computationally difficult to fit, particularly when the dimension of the data is large. To efficiently estimate the hub graphical models, we introduce a two-phase algorithm. The proposed algorithm first generates a good initial point via a dual alternating direction method of multipliers (ADMM), and then warm starts a semismooth Newton (SSN) based augmented Lagrangian method (ALM) to compute a solution that is accurate enough for practical tasks. We fully excavate the sparsity structure of the generalized Jacobian arising from the hubs in the graphical models, which ensures that the algorithm can obtain a nice solution very efficiently. Comprehensive experiments on both synthetic data and real data show that it obviously outperforms the existing state-of-the-art algorithms. In particular, in some high dimensional tasks, it can save more than 70\% of the execution time, meanwhile still achieves a high-quality estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08852 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learning the hub graphical Lasso model with the structured sparsity via an efficient algorithm Wang, Chengjing Tang, Peipei He, Wenling Lin, Meixia Optimization and Control Machine Learning Numerical Analysis Computation 90C25, 65K05, 90C06, 49M27, 90C20 Graphical models have exhibited their performance in numerous tasks ranging from biological analysis to recommender systems. However, graphical models with hub nodes are computationally difficult to fit, particularly when the dimension of the data is large. To efficiently estimate the hub graphical models, we introduce a two-phase algorithm. The proposed algorithm first generates a good initial point via a dual alternating direction method of multipliers (ADMM), and then warm starts a semismooth Newton (SSN) based augmented Lagrangian method (ALM) to compute a solution that is accurate enough for practical tasks. We fully excavate the sparsity structure of the generalized Jacobian arising from the hubs in the graphical models, which ensures that the algorithm can obtain a nice solution very efficiently. Comprehensive experiments on both synthetic data and real data show that it obviously outperforms the existing state-of-the-art algorithms. In particular, in some high dimensional tasks, it can save more than 70\% of the execution time, meanwhile still achieves a high-quality estimation. |
| title | Learning the hub graphical Lasso model with the structured sparsity via an efficient algorithm |
| topic | Optimization and Control Machine Learning Numerical Analysis Computation 90C25, 65K05, 90C06, 49M27, 90C20 |
| url | https://arxiv.org/abs/2308.08852 |