Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913171207356416 |
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| author | Chen, Guan-Yu Xie, Dong-Yue Yang, Xi |
| author_facet | Chen, Guan-Yu Xie, Dong-Yue Yang, Xi |
| contents | We propose a novel randomized framework for the estimation problem of large-scale linear statistical models, namely Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), which integrates Sketch-and-Solve and Iterative-Sketching methods for the first time. By iteratively constructing and solving sketched least-squares (LS) subproblems with increasing sketch sizes to achieve better precisions, SLSE-FRS gradually refines the estimators of the true parameter vector, ultimately producing high-precision estimators. We analyze the convergence properties of SLSE-FRS, and provide its efficient implementation. Numerical experiments show that SLSE-FRS outperforms the state-of-the-art methods, namely the Preconditioned Conjugate Gradient (PCG) method, and the Iterative Double Sketching (IDS) method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_06856 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models Chen, Guan-Yu Xie, Dong-Yue Yang, Xi Machine Learning Numerical Analysis 65F10, 65F20, 65K05, 68W20 We propose a novel randomized framework for the estimation problem of large-scale linear statistical models, namely Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), which integrates Sketch-and-Solve and Iterative-Sketching methods for the first time. By iteratively constructing and solving sketched least-squares (LS) subproblems with increasing sketch sizes to achieve better precisions, SLSE-FRS gradually refines the estimators of the true parameter vector, ultimately producing high-precision estimators. We analyze the convergence properties of SLSE-FRS, and provide its efficient implementation. Numerical experiments show that SLSE-FRS outperforms the state-of-the-art methods, namely the Preconditioned Conjugate Gradient (PCG) method, and the Iterative Double Sketching (IDS) method. |
| title | Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models |
| topic | Machine Learning Numerical Analysis 65F10, 65F20, 65K05, 68W20 |
| url | https://arxiv.org/abs/2509.06856 |