SIAM/ASA Journal on Uncertainty Quantification, Volume 9, Issue 2, Page 564-592, January 2021.
We introduce a class of acquisition functions for sample selection that lead to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The approach follows the paradigm of active learning, whereby existing samples of a black-box function are utilized to optimize the next most informative sample. The proposed method aims to take advantage of the fact that some input directions of the black-box function have a larger impact on the output than others, which is important especially for systems exhibiting rare and extreme events. The acquisition functions introduced in this work leverage the properties of the likelihood ratio, a quantity that acts as a probabilistic sampling weight and guides the active-learning algorithm toward regions of the input space that are deemed most relevant. We demonstrate the proposed approach in the uncertainty quantification of a hydrological system as well as the probabilistic quantification of rare events in dynamical systems and the identification of their precursors in up to 30 dimensions.

中文翻译：

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贝叶斯实验设计和不确定性量化的输出加权最优采样

SIAM / ASA不确定性量化期刊，第9卷，第2期，第564-592页，2021年1月。
我们介绍了用于样本选择的一类采集函数，这些函数可加快与贝叶斯实验设计和不确定性量化相关的应用程序的收敛速度。该方法遵循主动学习的范式，其中利用黑盒功能的现有样本来优化下一个信息量最大的样本。所提出的方法旨在利用以下事实：黑盒功能的某些输入方向比其他方向对输出的影响更大，这对于显示罕见事件和极端事件的系统尤其重要。这项工作中引入的获取功能利用了似然比的性质，似然比是一个概率采样权重，将主动学习算法引向输入空间中最相关的区域。