Low-Rank Thinning

Annabelle Michael Carrell; Albert Gong; Abhishek Shetty; Raaz Dwivedi; Lester Mackey

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arXiv · 2502.12063

Low-Rank Thinning

Annabelle Michael Carrell·Albert Gong·Abhishek Shetty·Raaz Dwivedi·Lester Mackey

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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.

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Annabelle Michael Carrell, Albert Gong, Abhishek Shetty, Raaz Dwivedi, Lester Mackey. 2025-02-17. Low-Rank Thinning. https://arxiv.org/abs/2502.12063

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