# Sampling Methods for Inner Product Sketching

arXiv: https://arxiv.org/abs/2309.16157 · HTML: https://mlsanity.com/paper/2309.16157/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2023.

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

- [Magneto: Combining Small and Large Language Models for Schema Matching](https://mlsanity.com/paper/2412.08194/) (2024)
- [Streaming Attention Approximation via Discrepancy Theory](https://mlsanity.com/paper/2502.07861/) (2025)
- [Coupling without Communication and Drafter-Invariant Speculative Decoding](https://mlsanity.com/paper/2408.07978/) (2024)
- [Efficient Sketching and Nearest Neighbor Search Algorithms for Sparse Vector Sets](https://mlsanity.com/paper/2509.24815/) (2025)

## Abstract (arXiv)

Recently, Bessa et al. (PODS 2023) showed that sketches based on coordinated weighted sampling theoretically and empirically outperform popular linear sketching methods like Johnson-Lindentrauss projection and CountSketch for the ubiquitous problem of inner product estimation. We further develop this finding by introducing and analyzing two alternative sampling-based methods. In contrast to the computationally expensive algorithm in Bessa et al., our methods run in linear time (to compute the sketch) and perform better in practice, significantly beating linear sketching on a variety of tasks. For example, they provide state-of-the-art results for estimating the correlation between columns in unjoined tables, a problem that we show how to reduce to inner product estimation in a black-box way. While based on known sampling techniques (threshold and priority sampling) we introduce significant new theoretical analysis to prove approximation guarantees for our methods.