多级Stein变分梯度下降的进一步分析及其在冰川冰模型贝叶斯推断中的应用
Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models
AI总结：
本研究扩展了多级Stein变分梯度下降的代价复杂度分析，使其适用于单级方法收敛速率依赖迭代参数的场景，并将该方法应用于冰川冰模型贝叶斯反问题，实现了数个数量级的加速。
摘要：
多级Stein变分梯度下降是一种基于粒子的变分推断方法，它利用具有不同计算成本和保真度的代理目标分布层次结构，从计算层面加快推断速度。本研究的贡献分为两方面。首先，本文对先前的代价复杂度分析进行了扩展，该扩展方法甚至适用于单级Stein变分梯度下降的指数收敛速率依赖于随迭代变化的参数的情况。其次，本文将多级Stein变分梯度下降应用于推断Arolla冰川离散化基底滑动系数场的大规模贝叶斯反问题。数值实验表明，与单级版本相比，多级版本实现了数个数量级的加速。
英文摘要：
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.
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