Wasserstein gradient flow for optimal probability measure decomposition

2024/06/03 by Han, Jiangze, Ryan, Christopher Thomas, Tong, Xin T. · 1 citation
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2406.00914

Abstract

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.

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