SILO: A scalable method to exploit screening in Gaussian process models with noise

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 x depends primarily on measurements nearest to x. 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, 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.

Biography:

Chris Geoga is an assistant professor at UW Madison’s Department of Statistics. He is interested in a broad range of topics at the intersection of applied mathematics and statistics and works with large-scale Gaussian process models to study complex dependence structure in data from the physical sciences.