# Wasserstein Measure Coresets

arXiv: https://arxiv.org/abs/1805.07412 · HTML: https://mlsanity.com/paper/1805.07412/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2018.

## Built on by (most cited first, 11 of 11)

- [Provable Data Subset Selection For Efficient Neural Network Training](https://mlsanity.com/paper/2303.05151/) (2023)
- [Federated Wasserstein Distance](https://mlsanity.com/paper/2310.01973/) (2023)
- [Fair Wasserstein Coresets](https://mlsanity.com/paper/2311.05436/) (2023)
- [Teaching Networks to Solve Optimization Problems](https://mlsanity.com/paper/2202.04104/) (2022)
- [FairWASP: Fast and Optimal Fair Wasserstein Pre-processing](https://mlsanity.com/paper/2311.00109/) (2023)
- [Scalable Learning from Probability Measures with Mean Measure Quantization](https://mlsanity.com/paper/2502.04907/) (2025)
- [Centroid Approximation for Bootstrap: Improving Particle Quality at Inference](https://mlsanity.com/paper/2110.08720/) (2021)
- [Coreset-Induced Conditional Velocity Flow Matching](https://mlsanity.com/paper/2605.12951/) (2026)
- [EMS Coreset: An Efficient Expectation-Maximization Algorithm for Sinkhorn Coreset](https://mlsanity.com/paper/2608.16101/) (2026)
- [WARP: Wasserstein-Aligned RAG for Population Opinions](https://mlsanity.com/paper/2608.22859/) (2026)
- [Measure Less, Know More: Self-Supervised Test-Time Feature Acquisition](https://mlsanity.com/paper/2610.03454/) (2026)

## Abstract (arXiv)

The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification. Coresets provide a principled way of summarizing a large dataset via a smaller one that is guaranteed to match the performance of the full data set on specific problems. Classical coresets, however, neglect the underlying data distribution, which is often continuous. We address this oversight by introducing Wasserstein measure coresets, an extension of coresets which by definition takes into account generalization. Our formulation of the problem, which essentially consists in minimizing the Wasserstein distance, is solvable via stochastic gradient descent. This yields an algorithm which simply requires sample access to the data distribution and is able to handle large data streams in an online manner. We validate our construction for inference and clustering.