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Randomized matrix algorithms have become workhorse tools in scientificcomputing and machine learning. To use these algorithms safely in applications,they should be coupled with posterior error estimates to assess the quality ofthe output. To meet this need, this paper proposes two diagnostics: aleave-one-out error estimator for randomized low-rank approximations and ajackknife resampling method to estimate the variance of the output of arandomized matrix computation. Both of these diagnostics are rapid to computefor randomized low-rank approximation algorithms such as the randomized SVD andNystr\"om, and they provide useful information that can be used to assess thequality of the computed output and guide algorithmic parameter choices.

Efficient error and variance estimation for randomized matrix computations