We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian
inference method that generalizes Stein Variational Gradient Descent (SVGD) to
Riemann manifold. The benefits are two-folds: (i) for inference tasks in
Euclidean spaces, RSVGD has the advantage over SVGD of utilizing information
geometry, and (ii) for inference tasks on Riemann manifolds, RSVGD brings the
unique advantages of SVGD to the Riemannian world. To appropriately transfer to
Riemann manifolds, we conceive novel and non-trivial techniques for RSVGD,
which are required by the intrinsically different characteristics of general
Riemann manifolds from Euclidean spaces. We also discover Riemannian Stein's
Identity and Riemannian Kernelized Stein Discrepancy. Experimental results show
the advantages over SVGD of exploring distribution geometry and the advantages
of particle-efficiency, iteration-effectiveness and approximation flexibility
over other inference methods on Riemann manifolds.

开发了一种称为 Riemannian Stein Variational Gradient Descent (RSVGD) 的贝叶斯推断方法，将 Stein Variational Gradient Descent (SVGD) 推广到 Riemann 流形上，利用信息几何学探索分布几何、提高粒子效率、迭代有效性和逼近灵活性，研究结果显示在 Riemann 流形上具有优势。