# Statistical properties of sketching algorithms

arXiv: https://arxiv.org/abs/1706.03665 · HTML: https://mlsanity.com/paper/1706.03665/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2017.

## Built on by (most cited first, 6 of 6)

- [Distributed Sketching for Randomized Optimization: Exact Characterization, Concentration and Lower Bounds](https://mlsanity.com/paper/2203.09755/) (2022)
- [Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learning](https://mlsanity.com/paper/2304.09154/) (2023)
- [Bayesian Data Sketching for Varying Coefficient Regression Models](https://mlsanity.com/paper/2506.00270/) (2025)
- [Error Estimation for Random Fourier Features](https://mlsanity.com/paper/2302.11174/) (2023)
- [Random-projection ensemble dimension reduction](https://mlsanity.com/paper/2410.04922/) (2024)
- [A Bayesian Vertical Federated Learning Framework for Multivariate Reduced-Rank High-Dimensional Regression](https://mlsanity.com/paper/2609.22654/) (2026)

## Abstract (arXiv)

Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a smaller surrogate dataset. Typically, inference proceeds on the compressed dataset. Sketching algorithms generally use random projections to compress the original dataset and this stochastic generation process makes them amenable to statistical analysis. We argue that the sketched data can be modelled as a random sample, thus placing this family of data compression methods firmly within an inferential framework. In particular, we focus on the Gaussian, Hadamard and Clarkson-Woodruff sketches, and their use in single pass sketching algorithms for linear regression with huge n. We explore the statistical properties of sketched regression algorithms and derive new distributional results for a large class of sketched estimators. A key result is a conditional central limit theorem for data oblivious sketches. An important finding is that the best choice of sketching algorithm in terms of mean square error is related to the signal to noise ratio in the source dataset. Finally, we demonstrate the theory and the limits of its applicability on two real datasets.