高维交互粒子采样的Radon-Wasserstein梯度流

This paper introduces a novel Radon-Wasserstein gradient flow framework designed to tackle the challenging problem of interacting-particle sampling in high dimensions. Traditional methods often encounter significant computational complexity and the curse of dimensionality when dealing with high-dimensional data. Our approach addresses this by leveraging the Radon transform to project high-dimensional probability distributions onto lower-dimensional spaces, thereby constructing a gradient flow under the Wasserstein distance metric. This dimensionality reduction effectively makes sampling and optimization feasible in high-dimensional settings. We rigorously prove the convergence properties of this gradient flow, providing robust theoretical guarantees. Through extensive numerical experiments, we demonstrate the superior performance of the Radon-Wasserstein gradient flow across various high-dimensional sampling tasks, including Bayesian inference and generative modeling. The proposed framework not only enhances sampling efficiency but also significantly reduces computational costs, offering a powerful tool for sampling complex high-dimensional distributions. Furthermore, we discuss the practical implications and potential applications of our method, outlining future research directions such as its integration with other Monte Carlo techniques and its broader applicability in diverse machine learning tasks.