Multilevel Stein variational gradient descent is a method for particle-based variational inference that leverages hierarchies of surrogate target distributions with varying costs and fidelity to computationally speed up inference. The contribution of this work is twofold. First, an extension of a previous cost complexity analysis is presented that applies even when the exponential convergence rate of single-level Stein variational gradient descent depends on iteration-varying parameters. Second, multilevel Stein variational gradient descent is applied to a large-scale Bayesian inverse problem of inferring discretized basal sliding coefficient fields of the Arolla glacier ice. The numerical experiments demonstrate that the multilevel version achieves orders of magnitude speedups compared to its single-level version.

多级斯坦因变分梯度下降是一种基于粒子的变分推理方法，它利用具有不同成本和保真度的代理目标分布的层次结构来在计算上加速推理。这项工作的贡献是双重的。首先，提出了先前成本复杂性分析的扩展，即使单级 Stein 变分梯度下降的指数收敛速度取决于迭代变化参数，该分析也适用。其次，将多级斯坦因变分梯度下降应用于推断阿罗拉冰川冰的离散基底滑动系数场的大规模贝叶斯逆问题。数值实验表明，与单级版本相比，多级版本实现了数量级的加速。