# Sequential Learning of Active Subspaces

arXiv: https://arxiv.org/abs/1907.11572 · HTML: https://mlsanity.com/paper/1907.11572/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2019.

## Built on by (most cited first, 16 of 16)

- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [Comparison of High-Dimensional Bayesian Optimization Algorithms on BBOB](https://mlsanity.com/paper/2303.00890/) (2023)
- [High-dimensional Bayesian Optimization with Group Testing](https://mlsanity.com/paper/2310.03515/) (2023)
- [Active Learning for Derivative-Based Global Sensitivity Analysis with Gaussian Processes](https://mlsanity.com/paper/2407.09739/) (2024)
- [Sensitivity Prewarping for Local Surrogate Modeling](https://mlsanity.com/paper/2101.06296/) (2021)
- [All Emulators are Wrong, Many are Useful, and Some are More Useful Than Others: A Reproducible Comparison of Computer Model Surrogates](https://mlsanity.com/paper/2512.09060/) (2025)
- [Leveraging Axis-Aligned Subspaces for High-Dimensional Bayesian Optimization with Group Testing](https://mlsanity.com/paper/2504.06111/) (2025)
- [Shared active subspace for multivariate vector-valued functions](https://mlsanity.com/paper/2401.02735/) (2024)
- [Combining additivity and active subspaces for high-dimensional Gaussian process modeling](https://mlsanity.com/paper/2402.03809/) (2024)
- [Active Subspaces in Infinite Dimension](https://mlsanity.com/paper/2510.11871/) (2025)
- [Surrogate Active Subspaces for Jump-Discontinuous Functions](https://mlsanity.com/paper/2310.10907/) (2023)
- [Regression Trees Know Calculus](https://mlsanity.com/paper/2405.13846/) (2024)
- [Actively Learning Joint Contours of Multiple Computer Experiments](https://mlsanity.com/paper/2512.13530/) (2025)
- [Calibrated Derivative-Process Sensitivity for Gaussian-Process Variable Selection](https://mlsanity.com/paper/2609.33549/) (2026)
- [Agentic High-Dimensional Bayesian Optimization with Hypothesis- and Evidence-Guided Search](https://mlsanity.com/paper/2609.34281/) (2026)

## Abstract (arXiv)

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.