Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models

TL;DR

This paper extends the theoretical analysis of multilevel Stein variational gradient descent and demonstrates its significant efficiency improvements in large-scale Bayesian glacier modeling.

Contribution

It provides a new cost complexity analysis for multilevel Stein variational gradient descent and applies it successfully to a large-scale glacier ice Bayesian inference problem.

Findings

Multilevel Stein variational gradient descent achieves orders of magnitude speedup.

The extended analysis applies even with iteration-dependent convergence rates.

Numerical experiments validate the efficiency in glacier ice Bayesian inference.

Abstract

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.