@inproceedings{carrell2025low-rank,
author = {Carrell, A. M. and Gong, Albert and Shetty, Abhishek and Dwivedi, Raaz and Mackey, Lester},
title = {Low-Rank Thinning},
booktitle = {ICML 2025},
year = {2025},
month = {February},
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.},
url = {http://approjects.co.za/?big=en-us/research/publication/low-rank-thinning/},
}