Fast algorithm for sparse least trimmed squares via trimmed-regularized reformulation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929529974423552 |
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| author | Yagishita, Shotaro |
| author_facet | Yagishita, Shotaro |
| contents | The least trimmed squares (LTS) is a reasonable formulation of robust regression whereas it suffers from high computational cost due to the nonconvexity and nonsmoothness of its objective function. The most frequently used FAST-LTS algorithm is particularly slow when a sparsity-inducing penalty such as the $\ell_1$ norm is added. This paper proposes a computationally inexpensive algorithm for the sparse LTS, which is based on the proximal gradient method with a reformulation technique. Proposed method is equipped with theoretical convergence preferred over existing methods. Numerical experiments show that our method efficiently yields small objective value. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_04554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast algorithm for sparse least trimmed squares via trimmed-regularized reformulation Yagishita, Shotaro Computation Optimization and Control Methodology The least trimmed squares (LTS) is a reasonable formulation of robust regression whereas it suffers from high computational cost due to the nonconvexity and nonsmoothness of its objective function. The most frequently used FAST-LTS algorithm is particularly slow when a sparsity-inducing penalty such as the $\ell_1$ norm is added. This paper proposes a computationally inexpensive algorithm for the sparse LTS, which is based on the proximal gradient method with a reformulation technique. Proposed method is equipped with theoretical convergence preferred over existing methods. Numerical experiments show that our method efficiently yields small objective value. |
| title | Fast algorithm for sparse least trimmed squares via trimmed-regularized reformulation |
| topic | Computation Optimization and Control Methodology |
| url | https://arxiv.org/abs/2410.04554 |