# Scalable Learning from Probability Measures with Mean Measure Quantization

arXiv: https://arxiv.org/abs/2502.04907 · HTML: https://mlsanity.com/paper/2502.04907/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 7 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations](https://mlsanity.com/paper/2008.09165/) (2020)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Principal Geodesic Analysis for Probability Measures under the Optimal Transport Metric](https://mlsanity.com/paper/1506.07944/) (2015)
- [Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learning](https://mlsanity.com/paper/2112.00423/) (2021)
- [Wasserstein Measure Coresets](https://mlsanity.com/paper/1805.07412/) (2018)
- [Improving Approximate Optimal Transport Distances using Quantization](https://mlsanity.com/paper/2102.12731/) (2021)
- [Low dimensional representation of multi-patient flow cytometry datasets using optimal transport for minimal residual disease detection in leukemia](https://mlsanity.com/paper/2407.17329/) (2024)

## Built on by (most cited first, 1 of 1)

- [Kernel K-means clustering of distributional data](https://mlsanity.com/paper/2509.18037/) (2025)

## Abstract (arXiv)

We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the measures have large support. We study a quantization-based approach in which all input measures are approximated by K-point discrete measures sharing a common support. We establish consistency of the resulting quantized measures. We further derive convergence guarantees for several OT-based downstream tasks computed from the quantized measures. Numerical experiments on synthetic and real datasets demonstrate that the proposed approach achieves performance comparable to individual quantization while substantially reducing runtime.