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Sequential Learning of Active Subspaces
Journal of Computational and Graphical Statistics ( IF 2.4 ) Pub Date : 2021-03-08 , DOI: 10.1080/10618600.2021.1874962
Nathan Wycoff 1 , Mickaël Binois 1 , Stefan M. Wild 1
Affiliation  

ABSTRACT

In recent years, active subspace methods (ASMs) have become a popular means of performing subspace sensitivity analysis on black-box functions. Naively applied, however, ASMs require gradient evaluations of the target function. In the event of noisy, expensive, or stochastic simulators, evaluating gradients via finite differencing may be infeasible. In such cases, often a surrogate model is employed, on which finite differencing is performed. When the surrogate model is a Gaussian process (GP), we show that the ASM estimator is available in closed form, rendering the finite-difference approximation unnecessary. We use our closed-form solution to develop acquisition functions focused on sequential learning tailored to sensitivity analysis on top of ASMs. We also show that the traditional ASM estimator may be viewed as a method of moments estimator for a certain class of GPs. We demonstrate how uncertainty on GP hyperparameters may be propagated to uncertainty on the sensitivity analysis, allowing model-based confidence intervals on the active subspace. Our methodological developments are illustrated on several examples. Supplementary files for this article are available online.



中文翻译:

主动子空间的顺序学习

摘要

近年来,主动子空间方法(ASM)已成为对黑盒函数进行子空间敏感性分析的流行手段。然而,天真地应用,ASM 需要目标函数的梯度评估。在嘈杂、昂贵或随机模拟器的情况下,通过有限差分评估梯度可能是不可行的。在这种情况下,通常采用代理模型,对其执行有限差分。当代理模型是高斯过程 (GP) 时,我们表明 ASM 估计器以封闭形式可用,从而不需要有限差分近似。我们使用我们的封闭式解决方案来开发专注于顺序学习的采集功能,这些功能专为基于 ASM 的敏感性分析量身定制。我们还表明,传统的 ASM 估计器可以被视为某一类 GP 的矩估计器方法。我们展示了 GP 超参数的不确定性如何传播到敏感性分析的不确定性,从而在活动子空间上允许基于模型的置信区间。我们的方法论发展在几个例子中得到了说明。本文的补充文件可在线获取。

更新日期:2021-03-08
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