Low-Rank Thinning
Abstract
The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially reducing the number of summary points. However, existing guarantees cover only a restricted range of distributions and kernel-based quality measures and suffer from pessimistic dimension dependence. To address these deficiencies, we introduce a new low-rank analysis of sub-Gaussian thinning that applies to any distribution and any kernel, guaranteeing high-quality compression whenever the kernel or data matrix is approximately low-rank. To demonstrate the broad applicability of the techniques, we design practical sub-Gaussian thinning approaches that improve upon the best known guarantees for approximating attention in transformers, accelerating stochastic gradient training through reordering, and distinguishing distributions in near-linear time.
Cite
@article{arxiv.2502.12063,
title = {Low-Rank Thinning},
author = {Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
journal= {arXiv preprint arXiv:2502.12063},
year = {2026}
}