Stein transport for Bayesian inference

Understand

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 $t=1$.