# Optimal Kernel Learning for Gaussian Process Models with High-Dimensional Input

arXiv: https://arxiv.org/abs/2502.16617 · HTML: https://mlsanity.com/paper/2502.16617/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 50 references that are in the map.
- First posted on arXiv 23 Feb 2025.

## Builds on (most cited first, 6 of 6)

- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [Convex Modeling of Interactions with Strong Heredity](https://mlsanity.com/paper/1410.3517/) (2014)
- [Dimension Reduction via Gaussian Ridge Functions](https://mlsanity.com/paper/1802.00515/) (2018)
- [Designs for Generalized Linear Models](https://mlsanity.com/paper/1510.05253/) (2015)
- [Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments](https://mlsanity.com/paper/1709.07064/) (2017)

## Abstract (arXiv)

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation involves too many input variables. For some simulation models, the outputs may only be significantly influenced by a small subset of the input variables, referred to as the ``active variables''. We propose an optimal kernel learning approach to identify these active variables, thereby overcoming GP model limitations and enhancing system understanding. Our method approximates the original GP model's covariance function through a convex combination of kernel functions, each utilizing low-dimensional subsets of input variables. Inspired by the Fedorov-Wynn algorithm from optimal design literature, we develop an optimal kernel learning algorithm to determine this approximation. We incorporate the effect heredity principle, a concept borrowed from the field of ``design and analysis of experiments'', to ensure sparsity in active variable selection. Through several examples, we demonstrate that the proposed method outperforms alternative approaches in correctly identifying active input variables and improving prediction accuracy. It is an effective solution for interpreting the surrogate GP regression and simplifying the complex underlying system.