# Sensitivity Prewarping for Local Surrogate Modeling

arXiv: https://arxiv.org/abs/2101.06296 · HTML: https://mlsanity.com/paper/2101.06296/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 107 references that are in the map.
- First posted on arXiv 15 Jan 2021.

## Builds on (most cited first, 16 of 16)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [Constant-Time Predictive Distributions for Gaussian Processes](https://mlsanity.com/paper/1803.06058/) (2018)
- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Scalable Log Determinants for Gaussian Process Kernel Learning](https://mlsanity.com/paper/1711.03481/) (2017)
- [Active Learning of Linear Embeddings for Gaussian Processes](https://mlsanity.com/paper/1310.6740/) (2013)
- [Permutation and Grouping Methods for Sharpening Gaussian Process Approximations](https://mlsanity.com/paper/1609.05372/) (2016)
- [Randomly Projected Additive Gaussian Processes for Regression](https://mlsanity.com/paper/1912.12834/) (2019)
- [A warped kernel improving robustness in Bayesian optimization via random embeddings](https://mlsanity.com/paper/1411.3685/) (2014)
- [Sequential Learning of Active Subspaces](https://mlsanity.com/paper/1907.11572/) (2019)
- [Scaled Vecchia approximation for fast computer-model emulation](https://mlsanity.com/paper/2005.00386/) (2020)
- [Locally induced Gaussian processes for large-scale simulation experiments](https://mlsanity.com/paper/2008.12857/) (2020)
- [Active Manifolds: A non-linear analogue to Active Subspaces](https://mlsanity.com/paper/1904.13386/) (2019)
- [Exploiting Active Subspaces in Global Optimization: How Complex is your Problem?](https://mlsanity.com/paper/1707.02533/) (2017)

## Built on by (most cited first, 4 of 4)

- [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)

## Abstract (arXiv)

In the continual effort to improve product quality and decrease operations costs, computational modeling is increasingly being deployed to determine feasibility of product designs or configurations. Surrogate modeling of these computer experiments via local models, which induce sparsity by only considering short range interactions, can tackle huge analyses of complicated input-output relationships. However, narrowing focus to local scale means that global trends must be re-learned over and over again. In this article, we propose a framework for incorporating information from a global sensitivity analysis into the surrogate model as an input rotation and rescaling preprocessing step. We discuss the relationship between several sensitivity analysis methods based on kernel regression before describing how they give rise to a transformation of the input variables. Specifically, we perform an input warping such that the "warped simulator" is equally sensitive to all input directions, freeing local models to focus on local dynamics. Numerical experiments on observational data and benchmark test functions, including a high-dimensional computer simulator from the automotive industry, provide empirical validation.