# Modern Subsampling Methods for Large-Scale Least Squares Regression

arXiv: https://arxiv.org/abs/2105.01552 · HTML: https://mlsanity.com/paper/2105.01552/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2021.

## Built on by (most cited first, 4 of 4)

- [An optimal transport approach for selecting a representative subsample with application in efficient kernel density estimation](https://mlsanity.com/paper/2206.01182/) (2022)
- [Adaptive and Stratified Subsampling for High-Dimensional Robust Estimation](https://mlsanity.com/paper/2410.12367/) (2024)
- [An adaptive subsampling method for large-sample feature screening](https://mlsanity.com/paper/2509.16085/) (2025)
- [Core-elements Subsampling for Alternating Least Squares](https://mlsanity.com/paper/2509.18024/) (2025)

## Abstract (arXiv)

Subsampling methods aim to select a subsample as a surrogate for the observed sample. As a powerful technique for large-scale data analysis, various subsampling methods are developed for more effective coefficient estimation and model prediction. This review presents some cutting-edge subsampling methods based on the large-scale least squares estimation. Two major families of subsampling methods are introduced, respectively, the randomized subsampling approach and the optimal subsampling approach. The former aims to develop a more effective data-dependent sampling probability, while the latter aims to select a deterministic subsample in accordance with certain optimality criteria. Real data examples are provided to compare these methods empirically, respecting both the estimation accuracy and the computing time.