A Scalable Method to Exploit Screening in Gaussian Process Models with Noise
提出一种基于EM算法的新方法，在高斯过程模型中利用筛选效应进行可扩展近似，尤其适用于Vecchia近似，并能处理测量噪声对筛选效应的削弱问题。
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 iid 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 (Vecchia), 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. Supplementary materials for this article are available online.