论文标题
随机矩阵计算的有效误差和方差估计
Efficient error and variance estimation for randomized matrix computations
论文作者
论文摘要
随机矩阵算法已成为科学计算和机器学习中的主力工具。要在应用中安全地使用这些算法，应将它们与后验错误估算相结合，以评估产出的质量。为了满足这一需求，本文提出了两个诊断：用于随机低级别近似值的剩余误差估计器和一种折刀重采样方法，以估计随机矩阵计算的输出的方差。这两种诊断都迅速计算用于随机低级别近似算法（例如随机SVD和随机NyStröm近似），并且它们提供了有用的信息，可用于评估计算出输出的质量和指导算法参数的选择。
Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the output. To meet this need, this paper proposes two diagnostics: a leave-one-out error estimator for randomized low-rank approximations and a jackknife resampling method to estimate the variance of the output of a randomized matrix computation. Both of these diagnostics are rapid to compute for randomized low-rank approximation algorithms such as the randomized SVD and randomized Nyström approximation, and they provide useful information that can be used to assess the quality of the computed output and guide algorithmic parameter choices.
