We introduce $\textit{Stein transport}$, a novel methodology for Bayesian inference designed to efficiently push an ensemble of particles along a predefined curve of tempered probability distributions. The driving vector field is chosen from a reproducing kernel Hilbert space and can be derived either through a suitable kernel ridge regression formulation or as an infinitesimal optimal transport map in the Stein geometry. The update equations of Stein transport resemble those of Stein variational gradient descent (SVGD), but introduce a time-varying score function as well as specific weights attached to the particles. While SVGD relies on convergence in the long-time limit, Stein transport reaches its posterior approximation at finite time $t=1$. Studying the mean-field limit, we discuss the errors incurred by regularisation and finite-particle effects, and we connect Stein transport to birth-death dynamics and Fisher-Rao gradient flows. In a series of experiments, we show that in comparison to SVGD, Stein transport not only often reaches more accurate posterior approximations with a significantly reduced computational budget, but that it also effectively mitigates the variance collapse phenomenon commonly observed in SVGD.

本研究针对贝叶斯推断中的效率问题，提出了新方法“Stein运输”，该方法通过预定的温度概率分布曲线有效推动粒子集。研究表明，与传统的Stein变分梯度下降方法相比，Stein运输在有限时间内获得更加精准的后验近似，同时显著减少了计算开销，且有效减轻了常见的方差崩溃现象。

Stein运输用于贝叶斯推断