Surrogate modeling and active subspaces have emerged as powerful paradigms in computational science and engineering. Porting such techniques to computational models in the social sciences brings into sharp relief their limitations in dealing with discontinuous simulators, such as Agent-Based Models, which have discrete outputs. Nevertheless, prior applied work has shown that surrogate estimates of active subspaces for such estimators can yield interesting results. But given that active subspaces are defined by way of gradients, it is not clear what quantity is being estimated when this methodology is applied to a discontinuous simulator. We begin this article by showing some pathologies that can arise when conducting such an analysis. This motivates an extension of active subspaces to discontinuous functions, clarifying what is actually being estimated in such analyses. We also conduct numerical experiments on synthetic test functions to compare Gaussian process estimates of active subspaces on continuous and discontinuous functions. Finally, we deploy our methodology on Flee, an agent-based model of refugee movement, yielding novel insights into which parameters of the simulation are most important across 8 displacement crises in Africa and the Middle East.

翻译：替代建模与主动子空间已成为计算科学与工程中的重要范式。将此类技术应用于社会科学领域的计算模型，暴露出其在处理具有离散输出的不连续模拟器（如基于智能体的模型）时的局限性。然而，先前应用研究表明，对此类估计器进行替代主动子空间估计可能产生有意义的结果。但鉴于主动子空间通过梯度定义，当该方法应用于不连续模拟器时，被估计量的确切含义尚不明确。本文首先展示进行此类分析时可能出现的一些病态现象，进而推动将主动子空间扩展至不连续函数，阐明此类分析中真正被估计的量。我们还在合成测试函数上进行数值实验，比较高斯过程对连续与不连续函数的主动子空间估计。最后，我们将该方法应用于Flee——一个难民流动的基于智能体模型，为非洲和中东8次流离失所危机中模拟参数的重要性排序提供了新见解。