# Mean Square Prediction Error of Misspecified Gaussian Process Models

arXiv: https://arxiv.org/abs/1811.06642 · HTML: https://mlsanity.com/paper/1811.06642/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2018.

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

- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications](https://mlsanity.com/paper/2109.02606/) (2021)
- [An Analysis of Safety Guarantees in Multi-Task Bayesian Optimization](https://mlsanity.com/paper/2503.08555/) (2025)
- [Error Bounds for Kernel-Based Linear System Identification with Unknown Hyperparameters](https://mlsanity.com/paper/2303.09842/) (2023)

## Abstract (arXiv)

Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide guarantees for application scenarios. Gaussian process regression represents one approach which provides such an indicator for the model confidence. However, this measure is only valid if the covariance function and its hyperparameters fit the underlying data generating process. In this paper, we derive an upper bound for the mean square prediction error of misspecified Gaussian process models based on a pseudo-concave optimization problem. We present application scenarios and a simulation to compare the derived upper bound with the true mean square error.