Low-Rank Thinning
Annabelle Michael Carrell, Albert Gong, Abhishek Shetty, Raaz Dwivedi, Lester Mackey
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.
BibTeX
@inproceedings{
carrell2025lowrank,
title={Low-Rank Thinning},
author={Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=iAkg2nVmvN}
}