Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models
This work provides incremental improvements to computational methods for large-scale Bayesian inference in glacier modeling, potentially aiding climate science applications.
The authors extended the cost complexity analysis of multilevel Stein variational gradient descent to handle iteration-varying convergence rates and applied it to a Bayesian inverse problem for inferring basal sliding coefficients of the Arolla glacier ice model, achieving orders of magnitude speedups compared to the single-level version.
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.