Multilevel Stein variational gradient descent with applications to Bayesian inverse problems
Multilevel Stein variational gradient descent with applications to Bayesian inverse problems
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发表时间：
2021-04
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通讯作者：
Terrence Alsup;Luca Venturi;B. Peherstorfer
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作者：
Terrence Alsup;Luca Venturi;B. Peherstorfer
这项工作提出了一个多层次的变化斯坦变分梯度下降，更有效地从目标分布的样本。关键成分是一系列分布，其保真度和成本不断增加，并向目标利益分布收敛。例如，这样的分布序列是由贝叶斯逆问题中的正向模型的更精细离散化水平的层次结构给出的。所提出的多级Stein变分梯度下降将大部分迭代移动到较低，较便宜的水平，目的是与仅使用最高级别分布的传统单级Stein变分梯度下降变体相比，仅需要在较高，较昂贵的水平上进行少量迭代。在一定的假设下，在平均场的限制，所提出的多级Stein方法的误差衰减的对数因子比单级对应的计算成本方面的错误。贝叶斯逆问题的数值实验表明，所提出的多层次斯坦方法相比，只使用最高级别的单级变体的一个数量级以上的加速比。
This work presents a multilevel variant of Stein variational gradient descent to more efficiently sample from target distributions. The key ingredient is a sequence of distributions with growing fidelity and costs that converges to the target distribution of interest. For example, such a sequence of distributions is given by a hierarchy of ever finer discretization levels of the forward model in Bayesian inverse problems. The proposed multilevel Stein variational gradient descent moves most of the iterations to lower, cheaper levels with the aim of requiring only a few iterations on the higher, more expensive levels when compared to the traditional, single-level Stein variational gradient descent variant that uses the highest-level distribution only. Under certain assumptions, in the mean-field limit, the error of the proposed multilevel Stein method decays by a log factor faster than the error of the single-level counterpart with respect to computational costs. Numerical experiments with Bayesian inverse problems show speedups of more than one order of magnitude of the proposed multilevel Stein method compared to the single-level variant that uses the highest level only.