Wasserstein gradient flow for optimal probability measure decomposition
This addresses optimization challenges in probability measure decomposition for machine learning tasks, but it appears incremental as it builds on existing Wasserstein methods.
The paper tackles the problem of decomposing a probability measure into K sub-measures to minimize loss functions for applications like clustering and user grouping, introducing Wasserstein gradient flow algorithms that are shown to converge and are validated with numerical results.
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.