# Prediction performance after learning in Gaussian process regression

arXiv: https://arxiv.org/abs/1606.03865 · HTML: https://mlsanity.com/paper/1606.03865/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2016.

## Built on by (most cited first, 2 of 2)

- [Neighborhood Sampling Does Not Learn the Same Graph Neural Network](https://mlsanity.com/paper/2509.22868/) (2025)
- [Adaptive Individual Uncertainty under Out-Of-Distribution Shift with Expert-Routed Conformal Prediction](https://mlsanity.com/paper/2510.15233/) (2025)

## Abstract (arXiv)

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean square-error (MSE). This approach, however, does not take into account that the statistical model is learned from the data. We show that this omission leads to a systematic underestimation of the prediction errors. Starting from a generalization of the Cram'er-Rao bound, we derive a more accurate MSE bound which provides a measure of uncertainty for prediction of Gaussian processes. The improved bound is easily computed and we illustrate it using synthetic and real data examples. of uncertainty for prediction of Gaussian processes and illustrate it using synthetic and real data examples.