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 Nystr\"om approximation, and they provide useful information that can be used to assess the quality of the computed output and guide algorithmic parameter choices.

翻译：随机矩阵算法已成为科学计算与机器学习领域的核心工具。为在应用中安全使用这些算法，需结合后验误差估计以评估输出质量。为此，本文提出两种诊断方法：针对随机低秩近似的留一法误差估计器，以及用于估计随机矩阵计算输出方差的刀切法重采样技术。这两种诊断方法在随机低秩近似算法（如随机SVD与随机Nystr\"om近似）中均能快速计算，并提供可用于评估计算输出质量、指导算法参数选择的有效信息。