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和机器学习中的关键工具。为确保这些算法在实际应用中的安全性，需配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：面向随机低秩近似的留一误差估计器，以及用于估计随机矩阵计算输出方差的刀切重抽样方法。这两种诊断方法针对随机奇异值分解、随机Nyström逼近等随机低秩近似算法均可快速计算，能提供评估计算输出质量的有用信息，并指导算法参数选择。