# Distributed Sketching on Data Partitions for OLS Regression

arXiv: https://arxiv.org/abs/2607.07888 · HTML: https://mlsanity.com/paper/2607.07888/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 6 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 3 of 3)

- [Distributed Sketching for Randomized Optimization: Exact Characterization, Concentration and Lower Bounds](https://mlsanity.com/paper/2203.09755/) (2022)
- [Distributed Least Squares in Small Space via Sketching and Bias Reduction](https://mlsanity.com/paper/2405.05343/) (2024)
- [GPU-Parallelizable Randomized Sketch-and-Precondition for Linear Regression using Sparse Sign Sketches](https://mlsanity.com/paper/2506.03070/) (2025)

## Abstract (arXiv)

This paper studies distributed sketching for ordinary least squares (OLS) regression, an approach that distributes small sketches of a large data set over multiple machines to separately construct OLS estimators and average them. Unlike prior studies that consider sketching on the whole data set, we consider sketching on partitioned subsets to further reduce computational cost. Under the fixed design setting, we characterize the exact excess loss of the averaged OLS estimator. Results show that this loss is comparable to the established loss for sketching on the whole data set when the divergence among subset covariances is small.