A fundamental procedure in the analysis of massive datasets is the construction of similarity graphs. Such graphs play a key role for many downstream tasks, including clustering, classification, graph learning, and nearest neighbor search.

Stein discrepancies (SDs) monitor convergence andnon-convergence inapprox-imate inference when exact integration and sampling are intractable. However,the computation of a Stein discrepancy can be prohibitive if the Stein operator - often a sum over likelihood terms or potentials - is expensive to evaluate.

In this paper, we propose a novel metric calledcompression ratioto capture the effect of PCA on high-dimensional noisy data.