A federated Kaczmarz algorithm
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913836520439808 |
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| author | Jeong, Halyun Needell, Deanna Wu, Chi-Hao |
| author_facet | Jeong, Halyun Needell, Deanna Wu, Chi-Hao |
| contents | In this paper, we propose a federated algorithm for solving large linear systems that is inspired by the classic randomized Kaczmarz algorithm. We provide convergence guarantees of the proposed method, and as a corollary of our analysis, we provide a new proof for the convergence of the classic randomized Kaczmarz method. We demonstrate experimentally the behavior of our method when applied to related problems. For underdetermined systems, we demonstrate that our algorithm can be used for sparse approximation. For inconsistent systems, we demonstrate that our algorithm converges to a horizon of the least squares solution. Finally, we apply our algorithm to real data and show that it is consistent with the selection of Lasso, while still offering the computational advantages of the Kaczmarz framework and thresholding-based algorithms in the federated setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A federated Kaczmarz algorithm Jeong, Halyun Needell, Deanna Wu, Chi-Hao Numerical Analysis 65F10 (Primary) In this paper, we propose a federated algorithm for solving large linear systems that is inspired by the classic randomized Kaczmarz algorithm. We provide convergence guarantees of the proposed method, and as a corollary of our analysis, we provide a new proof for the convergence of the classic randomized Kaczmarz method. We demonstrate experimentally the behavior of our method when applied to related problems. For underdetermined systems, we demonstrate that our algorithm can be used for sparse approximation. For inconsistent systems, we demonstrate that our algorithm converges to a horizon of the least squares solution. Finally, we apply our algorithm to real data and show that it is consistent with the selection of Lasso, while still offering the computational advantages of the Kaczmarz framework and thresholding-based algorithms in the federated setting. |
| title | A federated Kaczmarz algorithm |
| topic | Numerical Analysis 65F10 (Primary) |
| url | https://arxiv.org/abs/2505.09061 |