We consider doing Bayesian inference by minimizing the KL divergence on the 2-Wasserstein space $\mathcal{P}_2$. By exploring the Riemannian structure of $\mathcal{P}_2$, we develop two inference methods by simulating the gradient flow on $\mathcal{P}_2$ via updating particles, and an acceleration method that speeds up all such particle-simulation-based inference methods. Moreover we analyze the approximation flexibility of such methods, and conceive a novel bandwidth selection method for the kernel that they use. We note that $\mathcal{P}_2$ is quite abstract and general so that our methods can make closer approximation, while it still has a rich structure that enables practical implementation. Experiments show the effectiveness of the two proposed methods and the improvement of convergence by the acceleration method.

本文从Wasserstein梯度流的角度探索基于粒子的变分推断方法，并在理论和实践上做出了贡献，揭示了现有方法的假设和关系，并提出了一个加速框架和一个基于开发理论的有原则的带宽选择方法，这些方法利用了Wasserstein空间的几何，实验结果表明了加速框架的改善收敛和带宽选择方法提高了样本准确性。

理解和加速基于粒子的变分推断