可观测单调函数的自适应重构及其在不确定性量化中的应用
Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification
摘要：
出于对大类概率分布的偏差概率的严格的上界和下界的数值计算的愿望，我们提出了一种自适应算法的重建增加实值函数。虽然这个问题类似于保序回归的经典统计问题，但优化设置改变了问题的几个特征，并打开了自然的算法可能性。我们提出了我们的算法，建立充分条件的重建收敛到地面真理，并应用该方法合成测试用例和空气动力学设计的不确定性量化的一个现实世界的例子。
英文摘要：
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.
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