  The great success of modern machine learning models on large datasets is
contingent on extensive computational resources with high financial and
environmental costs. One way to address this is by extracting subsets that
generalize on par with the full data. In this work, we propose a general
framework, GRAD-MATCH, which finds subsets that closely match the gradient of
the training or validation set. We find such subsets effectively using an
orthogonal matching pursuit algorithm. We show rigorous theoretical and
convergence guarantees of the proposed algorithm and, through our extensive
experiments on real-world datasets, show the effectiveness of our proposed
framework. We show that GRAD-MATCH significantly and consistently outperforms
several recent data-selection algorithms and is Pareto-optimal with respect to
the accuracy-efficiency trade-off. The code of GRADMATCH is available as a part
of the CORDS toolkit: https://github.com/decile-team/cords.
