Mean Square Prediction Error of Misspecified Gaussian Process Models
This work addresses a specific issue in system identification and control for practitioners needing reliable uncertainty estimates, but it is incremental as it builds on existing Gaussian process methods.
The paper tackles the problem of unreliable model confidence in Gaussian process regression when the covariance function is misspecified, and derives an upper bound for the mean square prediction error through a pseudo-concave optimization problem, with validation via simulations.
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.