Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (J Mach Learn Res 17(1):1842–1879, 2016) based on randomized sketching matrices. However, it is computationally intensive due to the iterative sketch process. In this paper, we analyze the IHS algorithm under the unconstrained least squares problem setting and then propose a deterministic approach for improving IHS via A-optimal subsampling. Our contributions are threefold: (1) a good initial estimator based on the A-optimal design is suggested; (2) a novel ridged preconditioner is developed for repeated sketching; and (3) an exact line search method is proposed for determining the optimal step length adaptively. Extensive experimental results demonstrate that our proposed A-optimal IHS algorithm outperforms the existing accelerated IHS methods.

中文翻译：

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通过A最优子采样的自适应迭代Hessian草图

迭代黑森草图（IHS）是一种用于对大型数据建模的有效草图绘制方法。它最初是由Pilanci和Wainwright（J Mach Learn Res 17（1）：1842-1879，2016）基于随机草图矩阵提出的。但是，由于迭代草图过程，它的计算量很大。在本文中，我们分析了无约束最小二乘问题设置下的IHS算法，然后提出了一种通过A最优子采样改善IHS的确定性方法。我们的贡献是三方面的：（1）基于A的良好初始估计-建议最佳设计；（2）开发了一种新颖的脊状预处理器，用于重复草绘；（3）提出了一种精确的线搜索方法来自适应地确定最佳步长。大量的实验结果表明，我们提出的A最优IHS算法优于现有的加速IHS方法。