# Wasserstein gradient flow for optimal probability measure decomposition

arXiv: https://arxiv.org/abs/2406.00914 · HTML: https://mlsanity.com/paper/2406.00914/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 3 Jun 2024.

## Builds on (most cited first, 7 of 7)

- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization](https://mlsanity.com/paper/2102.11050/) (2021)
- [Policy Optimization as Wasserstein Gradient Flows](https://mlsanity.com/paper/1808.03030/) (2018)
- [Learning Strategies in Decentralized Matching Markets under Uncertain Preferences](https://mlsanity.com/paper/2011.00159/) (2020)
- [Sampling in Constrained Domains with Orthogonal-Space Variational Gradient Descent](https://mlsanity.com/paper/2210.06447/) (2022)
- [Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics](https://mlsanity.com/paper/1903.02273/) (2019)
- [Graph matching beyond perfectly-overlapping ErdHos--R'enyi random graphs](https://mlsanity.com/paper/2006.03284/) (2020)

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

- [Forward-Euler time-discretization for Wasserstein gradient flows can be wrong](https://mlsanity.com/paper/2406.08209/) (2024)

## Abstract (arXiv)

We examine the infinite-dimensional optimization problem of finding a decomposition of a probability measure into K probability sub-measures to minimize specific loss functions inspired by applications in clustering and user grouping. We analytically explore the structures of the support of optimal sub-measures and introduce algorithms based on Wasserstein gradient flow, demonstrating their convergence. Numerical results illustrate the implementability of our algorithms and provide further insights.