  The power of randomized algorithms in numerical methods have led to fast
solutions 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 as
sketching, when running SVD. While these approximation methods satisfy many
theoretical guarantees, we provide the first algorithmic implementations for
sketch-and-solve SVD problems on real-world, large-scale datasets. We provide a
comprehensive empirical evaluation of these algorithms and provide guidelines
on how to ensure accurate deployment to real-world data. As an application of
sketched SVD, we present Sketched Leverage Score Ordering, a technique for
determining the ordering of data in the training of neural networks. Our
technique is based on the distributed computation of leverage scores using
random projections. These computed leverage scores provide a flexible and
efficient method to determine the optimal ordering of training data without
manual intervention or annotations. We present empirical results on an
extensive set of experiments across image classification, language sentiment
analysis, and multi-modal sentiment analysis. Our method is faster compared to
standard randomized projection algorithms and shows improvements in convergence
and results.
