We consider the problem of active learning for global sensitivity analysis of expensive black-box functions. Our aim is to efficiently learn the importance of different input variables, e.g., in vehicle safety experimentation, we study the impact of the thickness of various components on safety objectives. Since function evaluations are expensive, we use active learning to prioritize experimental resources where they yield the most value. We propose novel active learning acquisition functions that directly target key quantities of derivative-based global sensitivity measures (DGSMs) under Gaussian process surrogate models. We showcase the first application of active learning directly to DGSMs, and develop tractable uncertainty reduction and information gain acquisition functions for these measures. Through comprehensive evaluation on synthetic and real-world problems, our study demonstrates how these active learning acquisition strategies substantially enhance the sample efficiency of DGSM estimation, particularly with limited evaluation budgets. Our work paves the way for more efficient and accurate sensitivity analysis in various scientific and engineering applications.

翻译：我们研究了针对昂贵黑箱函数全局敏感性分析的主动学习问题。我们的目标是高效地学习不同输入变量的重要性，例如在车辆安全实验中，我们研究不同部件厚度对安全目标的影响。由于函数评估成本高昂，我们采用主动学习来优先分配实验资源，以获取最大价值。我们提出了新颖的主动学习采集函数，这些函数直接针对高斯过程代理模型下基于导数的全局敏感性度量（DGSMs）的关键量。我们展示了主动学习在DGSMs中的首次应用，并为这些度量开发了可处理的不确定性减少和信息增益采集函数。通过对合成问题和实际问题的综合评估，我们的研究表明这些主动学习采集策略如何显著提高DGSM估计的样本效率，特别是在评估预算有限的情况下。我们的工作为各种科学和工程应用中更高效、更精确的敏感性分析铺平了道路。