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.

通过对不连续模拟器的分析，本研究将代理模型和主动子空间的方法扩展至社会科学领域，揭示了它们在处理不连续输出时的局限性，并通过在合成测试函数上进行数值实验，比较了连续和不连续函数上的高斯过程估计。最终，在模拟的中非和中东 8 个流离失所危机中，应用该方法于 Flee 代理模型中，得到了关于哪些参数最重要的全新见解。

跳跃不连续函数的替代活跃子空间

Surrogate Active Subspaces for Jump-Discontinuous Functions

Multivariate functions encountered in high-dimensional uncertainty
quantification problems often vary most strongly along a few dominant
directions in the input parameter space. We propose a gradient-based method for
detecting these directions and using them to construct ridge approximations of
such functions, in the case where the functions are vector-valued (e.g., taking
values in $\mathbb{R}^n$). The methodology consists of minimizing an upper
bound on the approximation error, obtained by subspace Poincar\'e inequalities.
We provide a thorough mathematical analysis in the case where the parameter
space is equipped with a Gaussian probability measure. The resulting method
generalizes the notion of active subspaces associated with scalar-valued
functions. A numerical illustration shows that using gradients of the function
yields effective dimension reduction. We also show how the choice of norm on
the codomain of the function has an impact on the function's low-dimensional
approximation.

提出一种基于梯度的方法，利用导向高维不确定性量化问题中重要方向，构建函数的岭近似，对于向量值函数来说。该方法最小化近似误差的上界，通过子空间 Poincare 不等式获得。在参数空间配备高斯概率测度的情况下，提供了彻底的数学分析，结果表明，使用函数的梯度可以有效地降低维度。还展示了如何选择函数定域的规范对函数的低维近似有影响。该方法推广了与标量值函数相关联的主动子空间的概念。