Wasserstein gradient flow for optimal probability measure decomposition
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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.
Key facts. Cited by 1 paper 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.
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7 of 27 references.
References · 7
- 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 426
- 2021Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimizationcited by 40
- 2018Policy Optimization as Wasserstein Gradient Flowscited by 34
- 2020Learning Strategies in Decentralized Matching Markets under Uncertain Preferencescited by 14
- 2022Sampling in Constrained Domains with Orthogonal-Space Variational Gradient Descentcited by 11
- 2019Mean Field Equilibrium: Uniqueness, Existence, and Comparative Staticscited by 2
- 2020Graph matching beyond perfectly-overlapping ErdHos--R'enyi random graphscited by 2
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Citing papers per year: 2024: 1.
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