{"ID":2873527,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.06856","arxiv_id":"2509.06856","title":"Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.06856","url_pdf":"https://arxiv.org/pdf/2509.06856v2","authors":"[\"Guan-Yu Chen\",\"Dong-Yue Xie\",\"Xi Yang\"]","published":"2025-09-08T16:23:58Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.NA\"]","methods":"[]","has_code":false}