# Evaluating the squared-exponential covariance function in Gaussian processes with integral observations

arXiv: https://arxiv.org/abs/1812.07319 · HTML: https://mlsanity.com/paper/1812.07319/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2018.

## Built on by (most cited first, 3 of 3)

- [Hierarchical Inducing Point Gaussian Process for Inter-domain Observations](https://mlsanity.com/paper/2103.00393/) (2021)
- [Using Distance Correlation for Efficient Bayesian Optimization](https://mlsanity.com/paper/2102.08993/) (2021)
- [Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priors](https://mlsanity.com/paper/2109.03457/) (2021)

## Abstract (arXiv)

This paper deals with the evaluation of double line integrals of the squared exponential covariance function. We propose a new approach in which the double integral is reduced to a single integral using the error function. This single integral is then computed with efficiently implemented numerical techniques. The performance is compared against existing state of the art methods and the results show superior properties in numerical robustness and accuracy per computation time.