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Sequential Learning of Active Subspaces

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, 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 Gaussian processes. We demonstrate how uncertainty on Gaussian process 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.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-02367750
Contributor : Mickaël Binois <>
Submitted on : Monday, November 18, 2019 - 10:45:34 AM
Last modification on : Thursday, May 20, 2021 - 9:12:02 AM

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  • HAL Id : hal-02367750, version 1
  • ARXIV : 1907.11572

Citation

Nathan Wycoff, Mickael Binois, Stefan M. Wild. Sequential Learning of Active Subspaces. 2019. ⟨hal-02367750⟩

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