# Measuring the robustness of Gaussian processes to kernel choice

arXiv: https://arxiv.org/abs/2106.06510 · HTML: https://mlsanity.com/paper/2106.06510/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 11 Jun 2021.

## Builds on (most cited first, 14 of 14)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Neural Tangents: Fast and Easy Infinite Neural Networks in Python](https://mlsanity.com/paper/1912.02803/) (2019)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Learning to Detect Sepsis with a Multitask Gaussian Process RNN Classifier](https://mlsanity.com/paper/1706.04152/) (2017)
- [Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness](https://mlsanity.com/paper/2001.10818/) (2020)
- [Validated Variational Inference via Practical Posterior Error Bounds](https://mlsanity.com/paper/1910.04102/) (2019)
- [Visualization in Bayesian workflow](https://mlsanity.com/paper/1709.01449/) (2017)
- [Robustness Guarantees for Bayesian Inference with Gaussian Processes](https://mlsanity.com/paper/1809.06452/) (2018)
- [An Improved Multi-Output Gaussian Process RNN with Real-Time Validation for Early Sepsis Detection](https://mlsanity.com/paper/1708.05894/) (2017)

## Built on by (most cited first, 6 of 6)

- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Boosting Offline Optimizers with Surrogate Sensitivity](https://mlsanity.com/paper/2503.04181/) (2025)
- [Physics Inspired Approaches To Understanding Gaussian Processes](https://mlsanity.com/paper/2305.10748/) (2023)
- [Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Models](https://mlsanity.com/paper/2503.02630/) (2025)
- [Online Identification of IT Systems through Active Causal Learning](https://mlsanity.com/paper/2509.02130/) (2025)
- [Kernel Model Validation: How To Do It, And Why You Should Care](https://mlsanity.com/paper/2509.15244/) (2025)

## Abstract (arXiv)

Gaussian processes (GPs) are used to make medical and scientific decisions, including in cardiac care and monitoring of atmospheric carbon dioxide levels. Notably, the choice of GP kernel is often somewhat arbitrary. In particular, uncountably many kernels typically align with qualitative prior knowledge (e.g. function smoothness or stationarity). But in practice, data analysts choose among a handful of convenient standard kernels (e.g. squared exponential). In the present work, we ask: Would decisions made with a GP differ under other, qualitatively interchangeable kernels? We show how to answer this question by solving a constrained optimization problem over a finite-dimensional space. We can then use standard optimizers to identify substantive changes in relevant decisions made with a GP. We demonstrate in both synthetic and real-world examples that decisions made with a GP can exhibit non-robustness to kernel choice, even when prior draws are qualitatively interchangeable to a user.