# A Scalable Method to Exploit Screening in Gaussian Process Models with Noise

arXiv: https://arxiv.org/abs/2208.06877 · HTML: https://mlsanity.com/paper/2208.06877/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2022.

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

- [Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization](https://mlsanity.com/paper/2301.13303/) (2023)
- [Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Data](https://mlsanity.com/paper/2405.14492/) (2024)

## Abstract (arXiv)

A common approach to approximating Gaussian log-likelihoods at scale exploits the fact that precision matrices can be well-approximated by sparse matrices in some circumstances. This strategy is motivated by the screening effect, which refers to the phenomenon in which the linear prediction of a process Z at a point x0 depends primarily on measurements nearest to x0. But simple perturbations, such as i.i.d. measurement noise, can significantly reduce the degree to which this exploitable phenomenon occurs. While strategies to cope with this issue already exist and are certainly improvements over ignoring the problem, in this work we present a new one based on the EM algorithm that offers several advantages. While in this work we focus on the application to Vecchia's approximation (1988), a particularly popular and powerful framework in which we can demonstrate true second-order optimization of M steps, the method can also be applied using entirely matrix-vector products, making it applicable to a very wide class of precision matrix-based approximation methods.