Alternating minimization for square root principal component pursuit
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909538222866432 |
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| author | Deng, Shengxiang Li, Xudong Zhang, Yangjing |
| author_facet | Deng, Shengxiang Li, Xudong Zhang, Yangjing |
| contents | Recently, the square root principal component pursuit (SRPCP) model has garnered significant research interest. It is shown in the literature that the SRPCP model guarantees robust matrix recovery with a universal, constant penalty parameter. While its statistical advantages are well-documented, the computational aspects from an optimization perspective remain largely unexplored. In this paper, we focus on developing efficient optimization algorithms for solving the SRPCP problem. Specifically, we propose a tuning-free alternating minimization (AltMin) algorithm, where each iteration involves subproblems enjoying closed-form optimal solutions. Additionally, we introduce techniques based on the variational formulation of the nuclear norm and Burer-Monteiro decomposition to further accelerate the AltMin method. Extensive numerical experiments confirm the efficiency and robustness of our algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00471 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alternating minimization for square root principal component pursuit Deng, Shengxiang Li, Xudong Zhang, Yangjing Optimization and Control Machine Learning 90C06, 90C25, 90C26, 90C30 Recently, the square root principal component pursuit (SRPCP) model has garnered significant research interest. It is shown in the literature that the SRPCP model guarantees robust matrix recovery with a universal, constant penalty parameter. While its statistical advantages are well-documented, the computational aspects from an optimization perspective remain largely unexplored. In this paper, we focus on developing efficient optimization algorithms for solving the SRPCP problem. Specifically, we propose a tuning-free alternating minimization (AltMin) algorithm, where each iteration involves subproblems enjoying closed-form optimal solutions. Additionally, we introduce techniques based on the variational formulation of the nuclear norm and Burer-Monteiro decomposition to further accelerate the AltMin method. Extensive numerical experiments confirm the efficiency and robustness of our algorithms. |
| title | Alternating minimization for square root principal component pursuit |
| topic | Optimization and Control Machine Learning 90C06, 90C25, 90C26, 90C30 |
| url | https://arxiv.org/abs/2501.00471 |