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In order to compute fast approximations to the singular value decompositions(SVD) of very large matrices, randomized sketching algorithms have become aleading approach. However, a key practical difficulty of sketching an SVD isthat the user does not know how far the sketched singular vectors/values arefrom the exact ones. Indeed, the user may be forced to rely on analyticalworst-case error bounds, which do not account for the unique structure of agiven problem. As a result, the lack of tools for error estimation often leadsto much more computation than is really necessary. To overcome thesechallenges, this paper develops a fully data-driven bootstrap method thatnumerically estimates the actual error of sketched singular vectors/values. Inparticular, this allows the user to inspect the quality of a rough initialsketched SVD, and then adaptively predict how much extra work is needed toreach a given error tolerance. Furthermore, the method is computationallyinexpensive, because it operates only on sketched objects, and it requires nopasses over the full matrix being factored. Lastly, the method is supported bytheoretical guarantees and a very encouraging set of experimental results.

Error Estimation for Sketched SVD via the Bootstrap