SIAM Journal on Matrix Analysis and Applications, Volume 42, Issue 3, Page 1199-1228, January 2021.
We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized dimensionality reduction transforms. We first develop a set of fast novel algorithms for rank estimation, column subset selection, and least squares preconditioning. We then describe the design and implementation of leverage score estimators based on these primitives. These estimators are also effective for rank deficient input, which is frequently the case in data analytics applications. We provide detailed complexity analyses for all algorithms as well as meaningful approximation bounds and comparisons with the state of the art. We conduct extensive numerical experiments to evaluate our algorithms and to illustrate their properties and performance using synthetic and real world datasets.

中文翻译：

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通过排名显示方法和随机化估计杠杆分数

SIAM 矩阵分析与应用杂志，第 42 卷，第 3 期，第 1199-1228 页，2021 年 1 月。
我们研究了用于估计任意秩的矩形密集或稀疏矩阵的统计杠杆分数的算法。我们的方法基于将秩揭示方法与密集和稀疏随机降维变换的组合相结合。我们首先开发了一组用于秩估计、列子集选择和最小二乘预处理的快速新颖算法。然后我们描述了基于这些原语的杠杆分数估计器的设计和实现。这些估计器对于排名不足的输入也很有效，这在数据分析应用程序中很常见。我们为所有算法提供了详细的复杂性分析以及有意义的近似边界和与现有技术的比较。