通过渐进式随机降维，快速实现高精度线性模型参数估计。
Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models
- 迭代构建并求解逐渐增大降维规模的最小二乘子问题。
- 在真实数据集上比PCG和IDS方法更快收敛且精度更高。
- 适合超大规模线性统计建模，尤其适用于资源受限场景。
我们提出一种新颖的随机化框架——带快速随机降维的顺序最小二乘估计器（SLSE-FRS），首次融合了Sketch-and-Solve与Iterative-Sketching方法。通过迭代构建并求解逐步增加降维规模的最小二乘（LS）子问题，逐步提升参数估计精度，最终获得高精度估计结果。我们分析了SLSE-FRS的收敛性，并给出了高效实现方案。数值实验表明，该方法在真实数据集上显著优于当前最先进的预处理共轭梯度（PCG）和迭代双重降维（IDS）方法。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。