论文标题
不完美观察的单调函数的自适应重建，并应用于不确定性定量
Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification
论文作者
论文摘要
由于渴望计算大量概率分布的偏差概率的严格上限和下限的愿望，我们提出了一种自适应算法，以重建增加实数函数。尽管此问题类似于等渗回归的经典统计问题，但优化设置设置会改变问题的几个特征，并打开了自然算法的可能性。我们介绍算法，为重建与地面真理的收敛建立足够的条件，并将方法应用于合成测试用例，并为空气设计的不确定性定量示例。
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, the optimisation setting alters several characteristics of the problem and opens natural algorithmic possibilities. We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method to synthetic test cases and a real-world example of uncertainty quantification for aerodynamic design.
