Sequential Learning of Active Subspaces
Sequential Learning of Active Subspaces
复制标题
主动子空间的顺序学习
DOI：
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复制
发表时间：
2019
影响因子：
2.4
通讯作者：
Stefan M. Wild
中科院分区：
文献类型：
--
作者：
Nathan Wycoff;M. Binois;Stefan M. Wild
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方法。然而，天真的应用，ASM 需要目标函数的梯度评估。在噪声、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，在其上执行有限差分。当代理模型是高斯过程（GP）时，我们证明 ASM 估计器可以封闭形式使用，从而不需要有限差分近似。我们使用封闭式解决方案来开发采集功能，重点是针对 ASM 之上的敏感性分析量身定制的顺序学习。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。我们演示了 GP 超参数的不确定性如何传播到敏感性分析的不确定性，从而允许活动子空间上基于模型的置信区间。我们的方法论发展通过几个例子来说明。本文的补充文件可在线获取。
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.
DOI：
10.1613/jair.4806
发表时间：
2013-01
期刊：
J. Artif. Intell. Res.
影响因子：
--
作者：
Ziyun Wang;M. Zoghi;F. Hutter;David Matheson;Nando de Freitas
通讯作者：
Ziyun Wang;M. Zoghi;F. Hutter;David Matheson;Nando de Freitas