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The power of randomized algorithms in numerical methods have led to fastsolutions which use the Singular Value Decomposition (SVD) as a core routine.However, given the large data size of modern and the modest runtime of SVD,most practical algorithms would require some form of approximation, such assketching, when running SVD. While these approximation methods satisfy manytheoretical guarantees, we provide the first algorithmic implementations forsketch-and-solve SVD problems on real-world, large-scale datasets. We provide acomprehensive empirical evaluation of these algorithms and provide guidelineson how to ensure accurate deployment to real-world data. As an application ofsketched SVD, we present Sketched Leverage Score Ordering, a technique fordetermining the ordering of data in the training of neural networks. Ourtechnique is based on the distributed computation of leverage scores usingrandom projections. These computed leverage scores provide a flexible andefficient method to determine the optimal ordering of training data withoutmanual intervention or annotations. We present empirical results on anextensive set of experiments across image classification, language sentimentanalysis, and multi-modal sentiment analysis. Our method is faster compared tostandard randomized projection algorithms and shows improvements in convergenceand results.

An Empirical Evaluation of Sketched SVD and its Application to Leverage Score Ordering