论文标题
贝叶斯实验设计和不确定性定量的输出加权最佳抽样
Output-Weighted Optimal Sampling for Bayesian Experimental Design and Uncertainty Quantification
论文作者
论文摘要
我们引入了用于样本选择的一类采集功能，从而导致与贝叶斯实验设计和不确定性定量相关的应用中的收敛速度更快。该方法遵循主动学习的范式，从而利用黑盒功能的现有样本来优化下一个最有用的样本。提出的方法旨在利用一个事实，即黑框函数的某些输入方向对产出的影响要比其他输出更大，这对于表现出罕见和极端事件的系统尤其重要。在本工作中引入的采集函数利用了似然比的性质，该数量充当了概率采样权重，并将主动学习算法引导到对输入空间区域的主动学习算法被认为是最相关的。我们证明了在水文系统的不确定性量化以及动态系统中稀有事件的概率定量及其前体的概率定量中，提出的方法的优越性。
We introduce a class of acquisition functions for sample selection that leads 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 towards regions of the input space that are deemed most relevant. We demonstrate superiority of 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.
